sr!com.femlab.server.ModelFileHeaderD%LtagstLcom/femlab/util/o;Ltypesq~LvrsntLcom/femlab/util/FlVersion;xpwsrcom.femlab.util.FlVersion%/B =IbuildImajorLdatetLjava/lang/String;Lextq~Lnameq~Lrcsq~L scriptNameq~xpwt COMSOL 3.2twt $Name: $t$Date: 2005/10/24 07:30:19 $xur[Ljava.lang.String;V{GxpBt modelinfotxfemtguitfem0tg69tg70tg66tg64tg68tg62tg67tg63tg65tfem14tfem14.0q~q~tfem16tfem16.0q~q~tg28tg22tg6tg19tg66tg25tg17tg67tg36tg15tg27tg16tg20tg23tg68tg24tg41tg26tg69tg30tg62tg32tg8tg40tg70tg21tg39tg63tg65tg3tg38tg64tg5tg35tg33tg7tg31tg4tg34tg18tg29tg1tg37t mfileinfot mfiletagsuq~ Bq~ t femstructt guistructq~Ltdrawq~Nq~Nq~Nq~Nq~Nq~Nq~Nq~Ntgeomtmeshtsolutiontxmeshq~Oq~Pq~Qq~Rtdrawq~Sq~Sq~Stdrawq~Sq~Sq~Tq~Sq~Sq~Sq~Sq~Sq~Sq~Tq~Sq~Sq~Sq~Tq~Sq~Tq~Sq~Sq~Sq~Tq~Sq~Sq~Tq~Tq~Sq~Sq~Tq~Sq~Sq~Sq~Sq~Sq~Sq~Sq~Sq~Stdrawq~Sq~Iq~Jxsrcom.femlab.api.client.ModelInfo^%Ldescrq~LdocURLq~[imaget[Bxpwur[BTxp6PNG  IHDRp IDATx mIZ׿Zv3mp$5t?ʓ$ nۍuPn2 9I%i&It>ހvP[F9EQAl򔲺9vP1jE_“BY;7~+dY7젬@F(i6HTY{nferg- xDh}FLBY/e'06 <;߯?eQR_k*s-_Jf~RfܹʭLĄϦt nA6xb1fES5V~fv};k2@htWJ{#L{D;4=~= _ nkAʃ5h۟޻//$1ߡW˖؏5ήí_.}Ds0$pIWhe/Ym@b́8)O:4GvQ'&!ݽp8!v U2yٻOKћ#ԧ ;J>ywm{^B>_`ݻWh%Хo+wmv5>ځp 19֌2"xSy9b9ro6CdGCCk?9U#Y-180SYP!9J:i;( 1 64O݃^'~,f#/8sWƷWt:uvW>܋-v$RiHtLs2?@V^EY.|kX@ydMvl-~d%3@V! 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@_oT?_ #u#(f޴5WWmQkur]27tGN|:rZ4`IUk<* OIJ29o#/{3߶aCg._\k_"ʛ|V&00>m  JȹwO3|3tƮT”(͜#a2f=X$0Ή=ǗvDm-GK~^j HJ0-þ(ZmP>+lZj-QXDVm yeՌg#F|0eHt19ѭC2j-"4ygI< ,L~@}+Vm!%Vx "d΃eBdC.4TGd4$2Ib8&DD2)g^볆Ռ') +X08 P<ٌ ]HH^=:` iOHom~pa:K';~p) !j,ANH(A ?՗Wrv@x YgYp?#38mGC ŀ)(U+y ^BAD4D Q592{<(%bW ><u-3᫣p1;ʷ~ܸw۞#3 i$:!*_gE<;Pr98dc-ȶiͿ4\5"C3|/SV̷;p`|ľ#{lTo5/C[p3D/*˞7x)xS[og&#[p4c F{ނ(*?P"|3oRCr=EށE?nZc蝧 }D9{Z"?I Wܙ牢#ZGйm_5Y쯒 E29T \90*Ws$ .(D-2'Ԥ6awVʍ7|."ّ9y#+Sς.3$riLlw޲_VS(2]|ZDz$Gh{ngv6fD>F0zȟq(8e(9܂d<#Ô]>TQ9؇`?L@NW>p!GF 6%5wM'~X[)R/q~y-;y=97EqWJԮx x|??}Y-s*:χd,b l`Ɔya\B^H7waSܙY3=.X~ u"Edgvdޛ_64Gڄ8 j'\%1NAۉ\SpBlP=UL$% [*,zKO=ج?*{ `'/-DWSV-%oe6 A̚\x@ܪBO{3ܙ7/"n)6F}b Jz[W1ЮW>5p>B'7yaq/ܿCәc\K+q-Lļ@d_ĈIRZjhG ?X&L0` [yZ/|Z4R_C9փCE^m<^TE9zA8乇mM`\ t;:n M}+mRe+4e+3ٖZAv[+NlSC% $I8Ъʾ辬-e=Km^B͡!u/"@5E" (Ga6 '$)yzxӬb1vqj ~WJ`5eE:c:KZ2&WSi tc6- +5)Uؿp䓣,,~sp/@4}fW)@gEX-5Bݤ*%@«dCb_ YT}g!4kVbi5h[.ΞdW"~<*J t:a#23UPp_M=0@'Yy#j*SCuYGJvW"/S$oӛ+OR:#nzGR K s),}#fXSG)/lgsdydkrr' BI&MmxJ+'xQ"J&v:&O7e7l+'h>磗d]vf c+kE=VGyJi]G̛n׳8Bh M:ltOX2LxGQf^!|UtUOgbkXo zgjas0׷'+rK枲ɖ- OyA8 xm\ϼ\yH턽{u-|={;إIg̋5yM|,|;~4/о#ݚ:YS!R9#=&rm䝞,AF5eBm%To7;yk"SJj="m5؝HA>\eE"Nʜ>Xx:(0F/rtzOk$nvɛGj=DvP+߫;, N# Iy_bBH?:.x˻vGwt;:(;:(;;:(;:(;:(;.߷'nIENDB`ppxuq~ tKQclear xfem clear vrsn vrsn.name = 'COMSOL 3.2'; vrsn.ext = ''; vrsn.major = 0; vrsn.build = 224; vrsn.rcs = '$Name: $'; vrsn.date = '$Date: 2005/10/24 07:30:19 $'; xfem.version = vrsn; xfem.id = 4; xfem.geomdata = 'geom'; xfem.eqvars = 'on'; xfem.cplbndeq = 'on'; xfem.cplbndsh = 'off'; xfem.geomvalid = 'on'; xfem.solvalid = 'on'; xfem.meshtime = 't'; clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.style = {{{'0'},{'0','0','255'}}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.name = {'tangential_H','normal_H','null'}; bnd.weak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'Hazi';'-Haxi*nx+Hrad*ny';'0'},{'0'; ... '0';'0'}}; bnd.style = {{{'0'},{'0','0','0'},{'solid'}},{{'0'},{'0','0','255'},{'dashed'}}, ... {{'0'},{'0','255','0'},{'dashdot'}}}; bnd.ind = [1,1,1,3,1,3,1,3,1,3,3,3,3,1,3,1,3,3,3,3,1,1,1,1]; appl.bnd = bnd; clear equ equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2; ... 3],[1;2;3],[1;2;3],[1;2;3]}; equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.usage = {1,1,1,1,1,1,1,1,1,1,1}; equ.name = {'uniax_diel_1','dielectric_0:vacuum','uniax_diel_2','uniax_diel_3', ... 'uniax_diel_4','uniax_diel_5','isotrop_diel_1','isotrop_diel_2','isotrop_diel_3', ... 'isotrop_diel_4','isotrop_diel_5'}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp2*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara2*M^2*test(Haxi)*Haxi)/x+eperp2*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara2*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp2*test(Hazix)*Hazix+epara2*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara2*eperp2)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp3*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara3*M^2*test(Haxi)*Haxi)/x+eperp3*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara3*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp3*test(Hazix)*Hazix+epara3*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara3*eperp3)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp4*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara4*M^2*test(Haxi)*Haxi)/x+eperp4*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara4*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp4*test(Hazix)*Hazix+epara4*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara4*eperp4)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp5*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara5*M^2*test(Haxi)*Haxi)/x+eperp5*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara5*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp5*test(Hazix)*Hazix+epara5*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara5*eperp5)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e1'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e2'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e3'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e4'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e5'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0'; ... '0'},{'0';'0';'0'}}; equ.style = {{{'0'},{'166','166','166'}},{{'0'},{'0','0','255'}},{{'0'},{'0', ... '255','0'}},{{'0'},{'0','255','255'}},{{'0'},{'255','0','255'}},{{'0'}, ... {'166','166','166'}},{{'0'},{'0','0','255'}},{{'0'},{'0','255','0'}},{{'0'}, ... {'0','255','255'}},{{'0'},{'255','0','255'}},{{'0'},{'166','166','166'}}}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; xfem.appl{1} = appl; xfem.geom = flbinary('fem14','geom','UWA_sloping_xband_res_c32_v5.mph'); xfem.mesh = flbinary('fem14.0','mesh','UWA_sloping_xband_res_c32_v5.mph'); xfem.sdim = {'x','y'}; xfem.frame = {'xy'}; xfem.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; xfem.gporder = 4; xfem.cporder = 2; xfem.sshape = 2; xfem.simplify = 'on'; xfem.border = 1; xfem.form = 'coefficient'; xfem.units = 'SI'; clear equ equ.shape = {[1;2;3],[1;2;3]}; equ.gporder = {{1;1;1},{1;1;1}}; equ.cporder = {{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0'},{'0';'0';'0'}}; equ.dinit = {{'0';'0';'0'},{'0';'0';'0'}}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+(test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'}}; equ.c = {{{'0'},{'0'},{'0'};{'0'},{'0'},{'0'};{'0'},{'0'},{'0'}},{{'0'}, ... {'0'},{'0'};{'0'},{'0'},{'0'};{'0'},{'0'},{'0'}}}; equ.a = {{'0','0','0';'0','0','0';'0','0','0'},{'0','0','0';'0','0','0'; ... '0','0','0'}}; equ.f = {{'0';'0';'0'},{'0';'0';'0'}}; equ.ea = {{'0','0','0';'0','0','0';'0','0','0'},{'0','0','0';'0','0','0'; ... '0','0','0'}}; equ.da = {{'0','0','0';'0','0','0';'0','0','0'},{'0','0','0';'0','0','0'; ... '0','0','0'}}; equ.al = {{{'0';'0'},{'0';'0'},{'0';'0'};{'0';'0'},{'0';'0'},{'0';'0'}; ... {'0';'0'},{'0';'0'},{'0';'0'}},{{'0';'0'},{'0';'0'},{'0';'0'};{'0';'0'}, ... {'0';'0'},{'0';'0'};{'0';'0'},{'0';'0'},{'0';'0'}}}; equ.be = {{{'0';'0'},{'0';'0'},{'0';'0'};{'0';'0'},{'0';'0'},{'0';'0'}; ... {'0';'0'},{'0';'0'},{'0';'0'}},{{'0';'0'},{'0';'0'},{'0';'0'};{'0';'0'}, ... {'0';'0'},{'0';'0'};{'0';'0'},{'0';'0'},{'0';'0'}}}; equ.ga = {{{'0';'0'};{'0';'0'};{'0';'0'}},{{'0';'0'};{'0';'0'};{'0';'0'}}}; equ.sshape = {[1],[1]}; equ.sshapedim = {{1;1;1},{1;1;1}}; equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {'absHradx_Axisymmetric_Dielectric_Resonator_Simulator',{'sqrt(Hradx^2+Hrady^2)', ... 'sqrt(Hradx^2+Hrady^2)'}, ... 'abscu1x_Axisymmetric_Dielectric_Resonator_Simulator',{'sqrt(cu1x^2+cu1y^2)', ... 'sqrt(cu1x^2+cu1y^2)'}, ... 'absHazix_Axisymmetric_Dielectric_Resonator_Simulator',{'sqrt(Hazix^2+Haziy^2)', ... 'sqrt(Hazix^2+Haziy^2)'}, ... 'abscu2x_Axisymmetric_Dielectric_Resonator_Simulator',{'sqrt(cu2x^2+cu2y^2)', ... 'sqrt(cu2x^2+cu2y^2)'}, ... 'absHaxix_Axisymmetric_Dielectric_Resonator_Simulator',{'sqrt(Haxix^2+Haxiy^2)', ... 'sqrt(Haxix^2+Haxiy^2)'}, ... 'abscu3x_Axisymmetric_Dielectric_Resonator_Simulator',{'sqrt(cu3x^2+cu3y^2)', ... 'sqrt(cu3x^2+cu3y^2)'}}; equ.expr = {'eperp',{'eperp1','1'}, ... 'epara',{'epara1','1'}}; equ.lock = [0,0,0,0,0,0,0,0,0]; equ.mlock = {[0,0,0,0,0,0,0,0,0]}; xfem.equ = equ; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'0';'0';'0'}}; bnd.q = {{'0','0','0';'0','0','0';'0','0','0'},{'0','0','0';'0','0','0'; ... '0','0','0'}}; bnd.h = {{'0','0','0';'0','0','0';'0','0','0'},{'0','0','0';'0','0','0'; ... '0','0','0'}}; bnd.g = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.r = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.shape = {[1;2;3],[1;2;3]}; bnd.sshape = {[1],[1]}; bnd.sshapedim = {{1;1;1},{1;1;1}}; bnd.gporder = {{1;1;1},{1;1;1}}; bnd.cporder = {{1;1;1},{1;1;1}}; bnd.init = {{'';'';''},{'';'';''}}; bnd.dinit = {{'';'';''},{'';'';''}}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; bnd.dim = {'Hrad','Hazi','Haxi'}; bnd.var = {'nx_Axisymmetric_Dielectric_Resonator_Simulator',{'nx','nx'}, ... 'ny_Axisymmetric_Dielectric_Resonator_Simulator',{'ny','ny'}}; bnd.expr = {}; bnd.lock = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; bnd.mlock = {[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]}; xfem.bnd = bnd; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.shape = {[1;2;3]}; pnt.sshape = {[1]}; pnt.sshapedim = {{1;1;1}}; pnt.init = {{'';'';''}}; pnt.dinit = {{'';'';''}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Hrad','Hazi','Haxi'}; pnt.var = {}; pnt.expr = {}; pnt.lock = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; pnt.mlock = {[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]}; xfem.pnt = pnt; xfem.var = {}; xfem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEnDens','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi', ... 'Drad','(Haxi*M-Haziy*x)/x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','(Hazi-Hrad*M+Hazix*x)/x', ... 'Erad','Drad/eperp', ... 'Eazi','Dazi/eperp', ... 'Eaxi','Daxi/epara', ... 'ElecMagSqrd','Erad*Erad+Eazi*Eazi+Eaxi*Eaxi', ... 'ElecEnDens','Erad*Drad+Eazi*Dazi+Eaxi*Daxi'}; clear descr descr.expr= {'Eaxi','axial component of electric field strength','DivH','divergence of magnetic field (should be zero!)','ElecEnDens','electric energy density','ElecMagSqrd','electric field strength magnitude squared','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','MagEnDens','magnetic energy density'}; xfem.descr = descr; clear draw draw.p.objs = {}; draw.p.name = {}; draw.c.objs = {}; draw.c.name = {}; draw.s.objs = {flbinary('g69','draw','UWA_sloping_xband_res_c32_v5.mph'),flbinary('g70','draw','UWA_sloping_xband_res_c32_v5.mph'),flbinary('g66','draw','UWA_sloping_xband_res_c32_v5.mph'),flbinary('g64','draw','UWA_sloping_xband_res_c32_v5.mph'),flbinary('g68','draw','UWA_sloping_xband_res_c32_v5.mph'),flbinary('g62','draw','UWA_sloping_xband_res_c32_v5.mph'),flbinary('g67','draw','UWA_sloping_xband_res_c32_v5.mph'),flbinary('g63','draw','UWA_sloping_xband_res_c32_v5.mph'),flbinary('g65','draw','UWA_sloping_xband_res_c32_v5.mph')}; draw.s.name = {'v4','v5','v1','s3','v3','s1','v2','s2','s4'}; xfem.draw = draw; xfem.const = {'c','299792458','fc','4*pi^2/c^2','alpha','1','M','14','delta_e','0*1e-3','e1','9.8*(1+delta_e)','e2','1.0','e3','1.0','e4','1.0','e5','1.0','delta_eperp1','0*1e-3','eperp1','9.2725*(1+delta_eperp1)','delta_epara1','0*1e-3','epara1','11.3486*(1+delta_epara1)','eperp2','1.0','epara2','1.0','eperp3','1.0','epara3','1.0','eperp4','1.0','epara4','1.0','eperp5','1.0','epara5','1.0','e_293K_alumina','9.8','eperp_4K_sapph_UWA','9.2725','epara_4K_sapph_UWA','11.3486','eperp_293K_sapph','9.407','epara_293K_sapph','11.62','eperp_4K_sapph_NPL','9.2848','epara_4K_sapph_NPL','11.3660'}; clear fcns xfem.functions = {}; descr = xfem.descr; descr.const= {'e_293K_alumina','relative permittivity of alumina at room temperature','e2','ditto for isotropic_dielectric_2','eperp2','relative permittivity of uniaxial_dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','c','speed of light (exact!)','delta_e','fractional increment (for determining filling factors)','e3','etc. ...','epara1','relative permittivity of uniaxial_dielectric_1 parallel to cylindrical axis','eperp3','etc.','delta_epara1','fractional increment (for determining filling factors)','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc. ...','e1','relative permittivity of isotropic_dielectric_1','eperp1','relative permittivity of uniaxial_dielectric_1 perpendicular to cylindrical axis','delta_eperp1','fractional increment (for determining filling factors)','eperp_4K_sapph_NPL','NPL values: fitted to resonance frequencies of NPL Cs HEMEX resonator','alpha','penalty coefficient on Div H'}; xfem.descr = descr; xfem.sol = flbinary('xfem','solution','UWA_sloping_xband_res_c32_v5.mph'); xfem.xmcases = [0]; xfem.mcases = [0]; flbinary clear; xfem.rulingmode = 'Axisymmetric_Dielectric_Resonator_Simulator'; xfem.solform = 'weak'; uq~ tgui.solvemodel.toutcomp='off'; gui.solvemodel.currsolver='eig'; gui.solvemodel.solveroption=''; gui.solvemodel.postsolver='eig'; gui.solvemodel.ntol='1.0E-6'; gui.solvemodel.maxiter='25'; gui.solvemodel.manualdamp='off'; gui.solvemodel.hnlin='off'; gui.solvemodel.initstep='1.0'; gui.solvemodel.minstep='1.0E-4'; gui.solvemodel.rstep='10.0'; gui.solvemodel.atol='0.0010'; gui.solvemodel.rtol='0.01'; gui.solvemodel.tlist='0:0.1:1'; gui.solvemodel.tout='tlist'; gui.solvemodel.tsteps='free'; gui.solvemodel.manualreassem='off'; gui.solvemodel.emassconst='on'; gui.solvemodel.massconst='on'; gui.solvemodel.loadconst='on'; gui.solvemodel.constrconst='on'; gui.solvemodel.jacobianconst='on'; gui.solvemodel.constrjacobianconst='on'; gui.solvemodel.manualstep='off'; gui.solvemodel.initialstep='0.0010'; gui.solvemodel.maxorder='5'; gui.solvemodel.maxstep='1.0'; gui.solvemodel.masssingular='maybe'; gui.solvemodel.consistent='2'; gui.solvemodel.estrat='0'; gui.solvemodel.complex='off'; gui.solvemodel.neigs='3'; gui.solvemodel.shift='0'; gui.solvemodel.maxeigit='300'; gui.solvemodel.etol='0.0'; gui.solvemodel.krylovdim='0'; gui.solvemodel.pname=''; gui.solvemodel.plist=''; gui.solvemodel.porder='1'; gui.solvemodel.manualparam='off'; gui.solvemodel.pinitstep='0.0'; gui.solvemodel.pminstep='0.0'; gui.solvemodel.pmaxstep='0.0'; gui.solvemodel.outform='auto'; gui.solvemodel.symmetric='on'; gui.solvemodel.symmhermit='symmetric'; gui.solvemodel.method='eliminate'; gui.solvemodel.nullfun='auto'; gui.solvemodel.blocksize='5000'; gui.solvemodel.uscale='auto'; gui.solvemodel.manscale=''; gui.solvemodel.rowscale='on'; gui.solvemodel.conjugate='off'; gui.solvemodel.complexfun='off'; gui.solvemodel.solfile='off'; gui.solvemodel.adaptgeom='currgeom'; gui.solvemodel.maxt='10000000'; gui.solvemodel.rmethod='longest'; gui.solvemodel.resorder='0'; gui.solvemodel.l2scale='1'; gui.solvemodel.l2staborder='2'; gui.solvemodel.eigselect='1'; gui.solvemodel.tpfun='fltpft'; gui.solvemodel.ngen='2'; gui.solvemodel.tpmult='1.7'; gui.solvemodel.tpworst='0.5'; gui.solvemodel.tpfract='0.5'; gui.solvemodel.autosolver='on'; gui.solvemodel.solcomp='Hazi,Haxi,Hrad'; gui.solvemodel.outcomp='Hazi,Haxi,Hrad'; gui.solvemodel.inittype='init_expr_currsol_radio'; gui.solvemodel.initsolnum='Automatic'; gui.solvemodel.inittime='0'; gui.solvemodel.utype='u_init_radio'; gui.solvemodel.usolnum='Automatic'; gui.solvemodel.utime='0'; gui.solvemodel.scriptcommands=''; gui.solvemodel.usescript='off'; gui.solvemodel.autoscript='off'; gui.solvemodel.linsolvernode.currlinsolver='spooles'; gui.solvemodel.linsolvernode.type='linsolver'; gui.solvemodel.linsolvernode.droptol='0.0'; gui.solvemodel.linsolvernode.thresh='0.1'; gui.solvemodel.linsolvernode.umfalloc='0.7'; gui.solvemodel.linsolvernode.preorder='mmd'; gui.solvemodel.linsolvernode.iter='2'; gui.solvemodel.linsolvernode.itol='1.0E-6'; gui.solvemodel.linsolvernode.rhob='400.0'; gui.solvemodel.linsolvernode.maxlinit='10000'; gui.solvemodel.linsolvernode.itrestart='50'; gui.solvemodel.linsolvernode.seconditer='1'; gui.solvemodel.linsolvernode.relax='1.0'; gui.solvemodel.linsolvernode.amgauto='3'; gui.solvemodel.linsolvernode.mglevels='6'; gui.solvemodel.linsolvernode.mgcycle='v'; gui.solvemodel.linsolvernode.maxcoarsedof='5000'; gui.solvemodel.linsolvernode.oocmemory='128.0'; gui.solvemodel.linsolvernode.oocfilename=''; gui.solvemodel.linsolvernode.modified='off'; gui.solvemodel.linsolvernode.fillratio='2.0'; gui.solvemodel.linsolvernode.respectpattern='on'; gui.solvemodel.linsolvernode.droptype='droptol'; gui.solvemodel.linsolvernode.vankavars=''; gui.solvemodel.linsolvernode.vankasolv='gmres'; gui.solvemodel.linsolvernode.vankatol='0.02'; gui.solvemodel.linsolvernode.vankarestart='100'; gui.solvemodel.linsolvernode.vankarelax='0.8'; gui.solvemodel.linsolvernode.mgauto='shape'; gui.solvemodel.linsolvernode.rmethod='regular'; gui.solvemodel.linsolvernode.coarseassem='on'; gui.solvemodel.linsolvernode.meshscale='2'; gui.solvemodel.linsolvernode.mgautolevels='2'; gui.solvemodel.linsolvernode.mgkeep='off'; gui.solvemodel.linsolvernode.mggeom='Geom1'; gui.solvemodel.linsolvernode.mcase0='on'; gui.solvemodel.linsolvernode.mgassem0='on'; gui.registry.general_currentmodel='Geom1'; gui.registry.general_currmeshcase='0'; gui.registry.general_savedonserver='off'; gui.registry.general_savedchanges='off'; gui.registry.general_rulingmode=''; gui.registry.general_incompletemfilehistory='off'; gui.registry.saved_license='1012177'; gui.registry.saved_version='COMSOL 3.2.0.224'; gui.registry.info_modelname=''; gui.registry.info_author=''; gui.registry.info_company=''; gui.registry.info_department=''; gui.registry.info_reference=''; gui.registry.info_url=''; gui.registry.info_saveddate='1187647492003'; gui.registry.info_creationdate='1141412764044'; gui.registry.info_modelresult=''; gui.reportregistry.report_contents='title=1;toc=1;modelprop=1;const=1;geometry=1;model_Geom1=1;mesh=1;appmode_Axisymmetric_Dielectric_Resonator_Simulator=1;lib_material=1;lib_section=1;coord=1;odesettings=1;intcoup=1;extrcoup=1;projcoup=1;percond=1;idcond=1;functions=1;interp=1;solver=1;post=1;equations=1;variables=1;'; gui.reportregistry.report_outputformat='html'; gui.reportregistry.report_filename='D:\My Documents\Work\Time Programme\Time 2003-2006\E03T 15 A high-flux rubidium\Topics\Finite Element Simulator\AxSim UWA Sloping Cryo Sapphire Resonator\11th April 2006\UWA_Sloping_Xband_Res_ElecStr_mo1.html'; gui.reportregistry.report_autoopen='on'; gui.reportregistry.report_paperformat='a4'; gui.reportregistry.report_includedefaults='off'; gui.reportregistry.report_template='none'; gui.reportregistry.report_showemptysections='off'; gui.flmodel{1}.modelname='Geom1'; gui.flmodel{1}.currmode='post'; gui.flmodel{1}.currappl='0'; gui.flmodel{1}.axis.xmin='-0.012116274782927584'; gui.flmodel{1}.axis.xmax='0.05702997310541651'; 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gui.flmodel{1}.postcamera.xmax='0.3357393470499441'; gui.flmodel{1}.postcamera.ymin='-0.2974238723509491'; gui.flmodel{1}.postcamera.ymax='0.2974238723509491'; gui.flmodel{1}.postcamera.camposx='0.2245684916124446'; gui.flmodel{1}.postcamera.camposy='0.24896500632166865'; gui.flmodel{1}.postcamera.camposz='3.3573934704994413'; gui.flmodel{1}.postcamera.camtargetx='0.2245684916124446'; gui.flmodel{1}.postcamera.camtargety='0.24896500632166865'; gui.flmodel{1}.postcamera.camtargetz='0.0'; gui.flmodel{1}.postcamera.camupx='0.0'; gui.flmodel{1}.postcamera.camupy='1.0'; gui.flmodel{1}.postcamera.camupz='0.0'; gui.flmodel{1}.lightmodel.headlight.type='point'; gui.flmodel{1}.lightmodel.headlight.name='headlight'; gui.flmodel{1}.lightmodel.headlight.enable='on'; gui.flmodel{1}.lightmodel.headlight.colorr='255'; gui.flmodel{1}.lightmodel.headlight.colorg='255'; gui.flmodel{1}.lightmodel.headlight.colorb='255'; gui.flmodel{1}.lightmodel.headlight.xpos='0.22456849'; gui.flmodel{1}.lightmodel.headlight.ypos='0.24896501'; 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gui.flmodel{1}.registry.camera_mouse='orbit'; gui.flmodel{1}.registry.camera_camconstr='none'; gui.flmodel{1}.registry.camera_mouseconstr='none'; gui.flmodel{1}.registry.camera_perspective='off'; gui.flmodel{1}.registry.camera_moveasbox='off'; gui.flmodel{1}.registry.draw_dialog='off'; gui.flmodel{1}.registry.draw_keepborders='on'; gui.flmodel{1}.registry.draw_keepedges='off'; gui.flmodel{1}.registry.draw_multi='off'; gui.flmodel{1}.registry.draw_snap2grid='on'; gui.flmodel{1}.registry.draw_snap2vtx='on'; gui.flmodel{1}.registry.draw_solid='on'; gui.flmodel{1}.registry.draw_workplane_coordsys='on'; gui.flmodel{1}.registry.draw_workplane_showgeom='on'; gui.flmodel{1}.registry.draw_projection='intersection'; gui.flmodel{1}.registry.transparency_value='1.0'; gui.flmodel{1}.registry.mesh_geomdetail='normal'; gui.flmodel{1}.registry.mesh_showquality='off'; gui.flmodel{1}.registry.post_cameraview='2'; gui.flmodel{1}.registry.graphics_scale='10.0'; gui.flmodel{1}.registry.render_bndarrow='on'; gui.flmodel{1}.registry.render_vertex='off'; gui.flmodel{1}.registry.render_edge='on'; gui.flmodel{1}.registry.render_face='off'; gui.flmodel{1}.registry.highlight_vertex='off'; gui.flmodel{1}.registry.highlight_edge='on'; gui.flmodel{1}.registry.highlight_face='on'; gui.flmodel{1}.meshparam.hmax=''; gui.flmodel{1}.meshparam.hmaxfact='1'; gui.flmodel{1}.meshparam.hgrad='1.3'; gui.flmodel{1}.meshparam.hcurve='0.3'; gui.flmodel{1}.meshparam.hcutoff='0.001'; gui.flmodel{1}.meshparam.hnarrow='1'; gui.flmodel{1}.meshparam.hpnt='10'; gui.flmodel{1}.meshparam.xscale='1.0'; gui.flmodel{1}.meshparam.yscale='1.0'; gui.flmodel{1}.meshparam.mlevel='sub'; gui.flmodel{1}.meshparam.mcase='0'; gui.flmodel{1}.meshparam.rmethod='regular'; gui.flmodel{1}.meshparam.hmaxvtx={'','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hgradvtx={'','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hgradedg={'','','','','','','','','','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hcurveedg={'','','','','','','','','','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hmaxedg={'','','','','','','','','','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hcutoffedg={'','','','','','','','','','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hgradsub={'','','','','','','','',''}; gui.flmodel{1}.meshparam.hmaxsub={'','','','','','','','',''}; gui.flmodel{1}.mapmeshparam.edgegroups={{'2','8','4','1'},{},{},{},{},{},{},{},{}}; gui.flmodel{1}.mapmeshparam.edgelem={1,'10',3,'25',5,'13',7,'7',14,'14',21,'17'}; gui.flmodel{1}.mapmeshparam.nedges='24'; gui.flmodel{1}.mapmeshparam.nelemtype=[1,1,1,1,1,1]; gui.flmodel{1}.postmodel.postplot.triplot='on'; gui.flmodel{1}.postmodel.postplot.tridata={'log(ElecMagSqrd+1e+0)'}; gui.flmodel{1}.postmodel.postplot.trirangeauto='on'; gui.flmodel{1}.postmodel.postplot.trirangemin='5.5921933750369135E-12'; gui.flmodel{1}.postmodel.postplot.trirangemax='13.099276680409837'; gui.flmodel{1}.postmodel.postplot.tricont='on'; gui.flmodel{1}.postmodel.postplot.triunit='1'; gui.flmodel{1}.postmodel.postplot.triheightdata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.triheightdatacheck='off'; gui.flmodel{1}.postmodel.postplot.trimap='jet'; gui.flmodel{1}.postmodel.postplot.trimapdepth='1024'; gui.flmodel{1}.postmodel.postplot.tribar='on'; gui.flmodel{1}.postmodel.postplot.triusemap='on'; gui.flmodel{1}.postmodel.postplot.tricolor='255,0,0'; gui.flmodel{1}.postmodel.postplot.tricoloring='interp'; gui.flmodel{1}.postmodel.postplot.trifill='fill'; gui.flmodel{1}.postmodel.postplot.contplot='off'; gui.flmodel{1}.postmodel.postplot.contdata={'log10(Eazi*Eazi+1e-3)'}; gui.flmodel{1}.postmodel.postplot.contcont='on'; gui.flmodel{1}.postmodel.postplot.contunit='1'; gui.flmodel{1}.postmodel.postplot.contheightdata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.contheightdatacheck='off'; gui.flmodel{1}.postmodel.postplot.contcolordata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.contcolorrangeauto='on'; gui.flmodel{1}.postmodel.postplot.contcolorrangemin=''; gui.flmodel{1}.postmodel.postplot.contcolorrangemax=''; gui.flmodel{1}.postmodel.postplot.contcolordatacheck='off'; gui.flmodel{1}.postmodel.postplot.contmap='cool'; gui.flmodel{1}.postmodel.postplot.contmapdepth='1024'; gui.flmodel{1}.postmodel.postplot.contbar='on'; gui.flmodel{1}.postmodel.postplot.contusemap='off'; gui.flmodel{1}.postmodel.postplot.contcolor='255,255,255'; gui.flmodel{1}.postmodel.postplot.contlevels='8'; gui.flmodel{1}.postmodel.postplot.contvectorlevels=''; gui.flmodel{1}.postmodel.postplot.contisvector='off'; gui.flmodel{1}.postmodel.postplot.linplot='off'; gui.flmodel{1}.postmodel.postplot.lindata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.linrangeauto='on'; gui.flmodel{1}.postmodel.postplot.linrangemin='-0.7800750712289763'; gui.flmodel{1}.postmodel.postplot.linrangemax='0.7797135542749551'; gui.flmodel{1}.postmodel.postplot.lincont='on'; gui.flmodel{1}.postmodel.postplot.linheightdata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.linheightdatacheck='off'; gui.flmodel{1}.postmodel.postplot.linmap='jet'; gui.flmodel{1}.postmodel.postplot.linmapdepth='1024'; gui.flmodel{1}.postmodel.postplot.linbar='on'; gui.flmodel{1}.postmodel.postplot.linusemap='on'; gui.flmodel{1}.postmodel.postplot.lincolor='255,0,0'; gui.flmodel{1}.postmodel.postplot.lincoloring='interp'; gui.flmodel{1}.postmodel.postplot.arrowplot='on'; gui.flmodel{1}.postmodel.postplot.arrowploton='sub'; gui.flmodel{1}.postmodel.postplot.arrowdata={'Erad','Eaxi'}; gui.flmodel{1}.postmodel.postplot.arrowbnddata={'Hrad','Hazi'}; gui.flmodel{1}.postmodel.postplot.arrowheightdata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.arrowheightdatacheck='off'; gui.flmodel{1}.postmodel.postplot.arrowxspacing='6'; gui.flmodel{1}.postmodel.postplot.arrowxvectorspacing=''; gui.flmodel{1}.postmodel.postplot.arrowxisvector='off'; gui.flmodel{1}.postmodel.postplot.arrowyspacing='14'; gui.flmodel{1}.postmodel.postplot.arrowyvectorspacing=''; gui.flmodel{1}.postmodel.postplot.arrowyisvector='off'; gui.flmodel{1}.postmodel.postplot.arrowtype='arrow'; gui.flmodel{1}.postmodel.postplot.arrowlength='proportional'; gui.flmodel{1}.postmodel.postplot.arrowcolor='255,255,255'; gui.flmodel{1}.postmodel.postplot.arrowautoscale='off'; gui.flmodel{1}.postmodel.postplot.arrowscale='1.3'; gui.flmodel{1}.postmodel.postplot.princplot='off'; gui.flmodel{1}.postmodel.postplot.princdata={'','','','','','','','','','','',''}; gui.flmodel{1}.postmodel.postplot.princheightdata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.princheightdatacheck='off'; gui.flmodel{1}.postmodel.postplot.princxspacing='8'; gui.flmodel{1}.postmodel.postplot.princxvectorspacing=''; gui.flmodel{1}.postmodel.postplot.princxisvector='off'; gui.flmodel{1}.postmodel.postplot.princyspacing='8'; gui.flmodel{1}.postmodel.postplot.princyvectorspacing=''; gui.flmodel{1}.postmodel.postplot.princyisvector='off'; gui.flmodel{1}.postmodel.postplot.princtype='arrow'; gui.flmodel{1}.postmodel.postplot.princlength='proportional'; gui.flmodel{1}.postmodel.postplot.princcolor='0,153,0'; gui.flmodel{1}.postmodel.postplot.princautoscale='on'; gui.flmodel{1}.postmodel.postplot.princscale='1'; gui.flmodel{1}.postmodel.postplot.flowplot='off'; gui.flmodel{1}.postmodel.postplot.flowplotas='lines'; gui.flmodel{1}.postmodel.postplot.flowdata={'Hrad','Hazi'}; gui.flmodel{1}.postmodel.postplot.flowtstartauto='on'; gui.flmodel{1}.postmodel.postplot.flowtstart=''; gui.flmodel{1}.postmodel.postplot.flowlines='20'; gui.flmodel{1}.postmodel.postplot.flowstart='sub'; gui.flmodel{1}.postmodel.postplot.flowstartx=''; gui.flmodel{1}.postmodel.postplot.flowstarty=''; gui.flmodel{1}.postmodel.postplot.flowisstartvector='off'; gui.flmodel{1}.postmodel.postplot.flowuseexpression='off'; gui.flmodel{1}.postmodel.postplot.flowcolor='255,0,0'; gui.flmodel{1}.postmodel.postplot.flowcolordata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.flowmap='jet'; gui.flmodel{1}.postmodel.postplot.flowmapdepth='1024'; gui.flmodel{1}.postmodel.postplot.flowbar='on'; gui.flmodel{1}.postmodel.postplot.flowpointcolor='255,0,0'; gui.flmodel{1}.postmodel.postplot.flowpointautoscale='on'; gui.flmodel{1}.postmodel.postplot.flowpointscale='1'; gui.flmodel{1}.postmodel.postplot.flowdroptype='once'; gui.flmodel{1}.postmodel.postplot.flowdroptimes=''; gui.flmodel{1}.postmodel.postplot.flowdropfreq=''; gui.flmodel{1}.postmodel.postplot.flowbnd='stick'; gui.flmodel{1}.postmodel.postplot.flowheightdata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.flowheightdatacheck='off'; gui.flmodel{1}.postmodel.postplot.poststreamoldcode='on'; gui.flmodel{1}.postmodel.postplot.flowtol='0.01'; gui.flmodel{1}.postmodel.postplot.flowstattol='0.01'; gui.flmodel{1}.postmodel.postplot.flowmaxtime='Inf'; gui.flmodel{1}.postmodel.postplot.flowmaxsteps='400'; gui.flmodel{1}.postmodel.postplot.flowback='on'; gui.flmodel{1}.postmodel.postplot.flownormal='off'; gui.flmodel{1}.postmodel.postplot.partplot='off'; gui.flmodel{1}.postmodel.postplot.partplotas='lines'; gui.flmodel{1}.postmodel.postplot.predefforces=''; gui.flmodel{1}.postmodel.postplot.partmass='1'; gui.flmodel{1}.postmodel.postplot.partforce={'','',''}; gui.flmodel{1}.postmodel.postplot.parttstartauto='on'; gui.flmodel{1}.postmodel.postplot.parttstart=''; gui.flmodel{1}.postmodel.postplot.partvelstart={'0','0','0'}; gui.flmodel{1}.postmodel.postplot.explicitcoord={'0','0'}; gui.flmodel{1}.postmodel.postplot.partuseexpression='off'; gui.flmodel{1}.postmodel.postplot.partcolor='255,0,0'; gui.flmodel{1}.postmodel.postplot.partcolordata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.partmap='jet'; gui.flmodel{1}.postmodel.postplot.partmapdepth='1024'; gui.flmodel{1}.postmodel.postplot.partbar='on'; gui.flmodel{1}.postmodel.postplot.partpointcolor='255,0,0'; gui.flmodel{1}.postmodel.postplot.partpointautoscale='on'; gui.flmodel{1}.postmodel.postplot.partpointscale='1'; gui.flmodel{1}.postmodel.postplot.partdroptype='once'; gui.flmodel{1}.postmodel.postplot.partdroptimes=''; gui.flmodel{1}.postmodel.postplot.partdropfreq=''; gui.flmodel{1}.postmodel.postplot.partbnd='stick'; gui.flmodel{1}.postmodel.postplot.partheightdata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.partheightdatacheck='off'; gui.flmodel{1}.postmodel.postplot.partrtol='0.001'; gui.flmodel{1}.postmodel.postplot.partatolmanual='off'; gui.flmodel{1}.postmodel.postplot.partatol={'',''}; gui.flmodel{1}.postmodel.postplot.partstepsizemanual='off'; gui.flmodel{1}.postmodel.postplot.parttendauto='on'; gui.flmodel{1}.postmodel.postplot.partmaxstepsauto='on'; gui.flmodel{1}.postmodel.postplot.partedgetol='0.001'; gui.flmodel{1}.postmodel.postplot.partvelvar={'partu','partv','partw'}; gui.flmodel{1}.postmodel.postplot.parttvar='partt'; gui.flmodel{1}.postmodel.postplot.partstatic='off'; gui.flmodel{1}.postmodel.postplot.partres='5'; gui.flmodel{1}.postmodel.postplot.maxminplot='off'; gui.flmodel{1}.postmodel.postplot.maxminsubdata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.maxminsubdatacheck='on'; gui.flmodel{1}.postmodel.postplot.maxminbnddata={'Hrad'}; gui.flmodel{1}.postmodel.postplot.maxminbnddatacheck='off'; gui.flmodel{1}.postmodel.postplot.geom='on'; gui.flmodel{1}.postmodel.postplot.roughplot='off'; gui.flmodel{1}.postmodel.postplot.autorefine='on'; gui.flmodel{1}.postmodel.postplot.refine='3'; gui.flmodel{1}.postmodel.postplot.geomnum={'Geom1'}; gui.flmodel{1}.postmodel.postplot.phase='0'; gui.flmodel{1}.postmodel.postplot.solnum='0'; gui.flmodel{1}.postmodel.postplot.selectvia='stored'; gui.flmodel{1}.postmodel.postplot.autotitle='on'; gui.flmodel{1}.postmodel.postplot.customtitle=''; gui.flmodel{1}.postmodel.postplot.smoothinternal='on'; gui.flmodel{1}.postmodel.postplot.useellogic='off'; gui.flmodel{1}.postmodel.postplot.ellogic=''; gui.flmodel{1}.postmodel.postplot.ellogictype='all'; gui.flmodel{1}.postmodel.postplot.deformplot='off'; gui.flmodel{1}.postmodel.postplot.deformsub='on'; gui.flmodel{1}.postmodel.postplot.deformbnd='on'; gui.flmodel{1}.postmodel.postplot.deformsubdata={'Hrad','Hazi'}; gui.flmodel{1}.postmodel.postplot.deformbnddata={'Hrad','Hazi'}; gui.flmodel{1}.postmodel.postplot.deformautoscale='on'; gui.flmodel{1}.postmodel.postplot.deformscale='0.002997'; gui.flmodel{1}.postmodel.postplot.animate_solnum='0'; gui.flmodel{1}.postmodel.postplot.animate_selectvia='stored'; gui.flmodel{1}.postmodel.postplot.filetype='AVI'; gui.flmodel{1}.postmodel.postplot.width='640'; gui.flmodel{1}.postmodel.postplot.height='480'; gui.flmodel{1}.postmodel.postplot.fps='10'; gui.flmodel{1}.postmodel.postplot.statfunctype='full'; gui.flmodel{1}.postmodel.postplot.statnframes='11'; gui.flmodel{1}.postmodel.postplot.reverse='off'; gui.flmodel{1}.postmodel.postplot.movieinmatlab='off'; gui.flmodel{1}.postmodel.postplot.copyaxis='off'; gui.flmodel{1}.postmodel.intdata{1}.intdata={'Hrad'}; gui.flmodel{1}.postmodel.intdata{1}.phase='0'; gui.flmodel{1}.postmodel.intdata{1}.solnum='0'; gui.flmodel{1}.postmodel.intdata{1}.selectvia='stored'; gui.flmodel{1}.postmodel.intdata{2}.order='4'; gui.flmodel{1}.postmodel.intdata{2}.autoorder='on'; gui.flmodel{1}.postmodel.intdata{2}.multiplyexpr='off'; gui.flmodel{1}.postmodel.intdata{2}.intdata={'2*pi*x*(Hazi^2*(nx^2+ny^2)+(Haxi*nx-Hrad*ny)^2)'}; gui.flmodel{1}.postmodel.intdata{2}.phase='0'; gui.flmodel{1}.postmodel.intdata{2}.solnum='0'; gui.flmodel{1}.postmodel.intdata{2}.selectvia='stored'; gui.flmodel{1}.postmodel.intdata{3}.order='4'; gui.flmodel{1}.postmodel.intdata{3}.autoorder='on'; gui.flmodel{1}.postmodel.intdata{3}.multiplyexpr='off'; gui.flmodel{1}.postmodel.intdata{3}.intdata={'2*pi*x*MagEnDens'}; gui.flmodel{1}.postmodel.intdata{3}.phase='0'; gui.flmodel{1}.postmodel.intdata{3}.solnum='0'; gui.flmodel{1}.postmodel.intdata{3}.selectvia='stored'; gui.flmodel{1}.postmodel.domainplot.colordata={'Hrad'}; gui.flmodel{1}.postmodel.domainplot.colorrangeauto='on'; gui.flmodel{1}.postmodel.domainplot.colorrangemin=''; gui.flmodel{1}.postmodel.domainplot.colorrangemax=''; gui.flmodel{1}.postmodel.domainplot.colorcont='on'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacemap='jet'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacemapdepth='1024'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacebar='on'; gui.flmodel{1}.postmodel.domainplot.surfacesurfaceusemap='on'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacecolor='255,0,0'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacecoloring='interp'; gui.flmodel{1}.postmodel.domainplot.surfacesurfacefill='fill'; gui.flmodel{1}.postmodel.domainplot.extrusion='off'; gui.flmodel{1}.postmodel.domainplot.lineyaxisdata={'Hrad'}; gui.flmodel{1}.postmodel.domainplot.lineyaxiscont='on'; gui.flmodel{1}.postmodel.domainplot.linexaxisxaxistype='arc'; gui.flmodel{1}.postmodel.domainplot.linexaxisuseexpr='off'; gui.flmodel{1}.postmodel.domainplot.linexaxisdata={'Hrad'}; gui.flmodel{1}.postmodel.domainplot.linelinestyle='solid'; gui.flmodel{1}.postmodel.domainplot.linelinecolor='cyclecolor'; gui.flmodel{1}.postmodel.domainplot.linelinemarker='none'; gui.flmodel{1}.postmodel.domainplot.linelegend='off'; gui.flmodel{1}.postmodel.domainplot.linecolor='255,0,0'; gui.flmodel{1}.postmodel.domainplot.linesurfacemap='jet'; gui.flmodel{1}.postmodel.domainplot.linesurfacemapdepth='1024'; gui.flmodel{1}.postmodel.domainplot.linesurfacebar='on'; gui.flmodel{1}.postmodel.domainplot.linesurfaceusemap='on'; gui.flmodel{1}.postmodel.domainplot.linesurfacecolor='255,0,0'; gui.flmodel{1}.postmodel.domainplot.linesurfacecoloring='interp'; gui.flmodel{1}.postmodel.domainplot.linesurfacefill='fill'; gui.flmodel{1}.postmodel.domainplot.pointyaxisdata={'Hrad'}; gui.flmodel{1}.postmodel.domainplot.pointxxaxistype=''; gui.flmodel{1}.postmodel.domainplot.pointxuseexpr='off'; gui.flmodel{1}.postmodel.domainplot.pointxdata={'Hrad'}; gui.flmodel{1}.postmodel.domainplot.pointlinestyle='solid'; gui.flmodel{1}.postmodel.domainplot.pointlinecolor='cyclecolor'; gui.flmodel{1}.postmodel.domainplot.pointlinemarker='none'; gui.flmodel{1}.postmodel.domainplot.pointlegend='off'; gui.flmodel{1}.postmodel.domainplot.pointcolor='255,0,0'; gui.flmodel{1}.postmodel.domainplot.crossdispcolor='255,0,0'; gui.flmodel{1}.postmodel.domainplot.phase='0'; gui.flmodel{1}.postmodel.domainplot.solnum='0'; gui.flmodel{1}.postmodel.domainplot.selectvia='stored'; gui.flmodel{1}.postmodel.domainplot.autotitle='on'; gui.flmodel{1}.postmodel.domainplot.customtitle=''; gui.flmodel{1}.postmodel.domainplot.autolabelx='on'; gui.flmodel{1}.postmodel.domainplot.customlabelx=''; gui.flmodel{1}.postmodel.domainplot.autolabely='on'; gui.flmodel{1}.postmodel.domainplot.customlabely=''; gui.flmodel{1}.postmodel.domainplot.axistype={'lin','lin'}; gui.flmodel{1}.postmodel.domainplot.smoothinternal='on'; gui.flmodel{1}.postmodel.domainplot.autorefine='on'; gui.flmodel{1}.postmodel.domainplot.refine='3'; gui.flmodel{1}.postmodel.domainplot.plottypeind='0'; gui.flmodel{1}.postmodel.crossplot.extrusion='off'; gui.flmodel{1}.postmodel.crossplot.lineyaxisdata={'Hrad'}; gui.flmodel{1}.postmodel.crossplot.linexaxisxaxistype='arc'; gui.flmodel{1}.postmodel.crossplot.linexaxisuseexpr='off'; gui.flmodel{1}.postmodel.crossplot.linexaxisdata={'Hrad'}; gui.flmodel{1}.postmodel.crossplot.linelinestyle='solid'; gui.flmodel{1}.postmodel.crossplot.linelinecolor='cyclecolor'; gui.flmodel{1}.postmodel.crossplot.linelinemarker='none'; gui.flmodel{1}.postmodel.crossplot.linelegend='off'; gui.flmodel{1}.postmodel.crossplot.linecolor='255,0,0'; gui.flmodel{1}.postmodel.crossplot.linesurfacemap='jet'; gui.flmodel{1}.postmodel.crossplot.linesurfacemapdepth='1024'; gui.flmodel{1}.postmodel.crossplot.linesurfacebar='on'; gui.flmodel{1}.postmodel.crossplot.linesurfaceusemap='on'; gui.flmodel{1}.postmodel.crossplot.linesurfacecolor='255,0,0'; gui.flmodel{1}.postmodel.crossplot.linesurfacecoloring='interp'; gui.flmodel{1}.postmodel.crossplot.linesurfacefill='fill'; gui.flmodel{1}.postmodel.crossplot.lineresolution='200'; gui.flmodel{1}.postmodel.crossplot.linecoord={'0','1','0','0'}; gui.flmodel{1}.postmodel.crossplot.linelevels='5'; gui.flmodel{1}.postmodel.crossplot.linevectorlevels=''; gui.flmodel{1}.postmodel.crossplot.lineisvector='off'; gui.flmodel{1}.postmodel.crossplot.lineactive='off'; gui.flmodel{1}.postmodel.crossplot.pointyaxisdata={'Hrad'}; gui.flmodel{1}.postmodel.crossplot.pointxxaxistype=''; gui.flmodel{1}.postmodel.crossplot.pointxuseexpr='off'; gui.flmodel{1}.postmodel.crossplot.pointxdata={'Hrad'}; gui.flmodel{1}.postmodel.crossplot.pointlinestyle='solid'; gui.flmodel{1}.postmodel.crossplot.pointlinecolor='cyclecolor'; gui.flmodel{1}.postmodel.crossplot.pointlinemarker='none'; gui.flmodel{1}.postmodel.crossplot.pointlegend='off'; gui.flmodel{1}.postmodel.crossplot.pointcolor='255,0,0'; gui.flmodel{1}.postmodel.crossplot.pointcoord={'0','0'}; gui.flmodel{1}.postmodel.crossplot.crossdispcolor='255,0,0'; gui.flmodel{1}.postmodel.crossplot.phase='0'; gui.flmodel{1}.postmodel.crossplot.solnum='0'; gui.flmodel{1}.postmodel.crossplot.selectvia='stored'; gui.flmodel{1}.postmodel.crossplot.autotitle='on'; gui.flmodel{1}.postmodel.crossplot.customtitle=''; gui.flmodel{1}.postmodel.crossplot.autolabelx='on'; gui.flmodel{1}.postmodel.crossplot.customlabelx=''; gui.flmodel{1}.postmodel.crossplot.autolabely='on'; gui.flmodel{1}.postmodel.crossplot.customlabely=''; gui.flmodel{1}.postmodel.crossplot.axistype={'lin','lin'}; gui.flmodel{1}.postmodel.crossplot.plottypeind='0'; gui.flmodel{1}.postmodel.dataexport.pntdata={'Hrad'}; gui.flmodel{1}.postmodel.dataexport.pntlocation='element'; gui.flmodel{1}.postmodel.dataexport.pntlagorder='2'; gui.flmodel{1}.postmodel.dataexport.bnddata={'Hrad'}; gui.flmodel{1}.postmodel.dataexport.bndcont='on'; gui.flmodel{1}.postmodel.dataexport.bndlocation='element'; gui.flmodel{1}.postmodel.dataexport.bndlagorder='2'; gui.flmodel{1}.postmodel.dataexport.subdata={'Hrad'}; gui.flmodel{1}.postmodel.dataexport.subcont='on'; gui.flmodel{1}.postmodel.dataexport.subxspacing='10'; gui.flmodel{1}.postmodel.dataexport.subxvectorspacing=''; gui.flmodel{1}.postmodel.dataexport.subxisvector='off'; gui.flmodel{1}.postmodel.dataexport.subyspacing='10'; gui.flmodel{1}.postmodel.dataexport.subyvectorspacing=''; gui.flmodel{1}.postmodel.dataexport.subyisvector='off'; gui.flmodel{1}.postmodel.dataexport.sublocation='element'; gui.flmodel{1}.postmodel.dataexport.sublagorder='2'; gui.flmodel{1}.postmodel.dataexport.phase='0'; gui.flmodel{1}.postmodel.dataexport.solnum='0'; gui.flmodel{1}.postmodel.dataexport.selectvia='stored'; gui.flmodel{1}.postmodel.dataexport.exportformat='ptd'; gui.flmodel{1}.postmodel.dataexport.exportedim='2'; gui.flmodel{1}.postmodel.dataexport.struct='off'; gui.flmodel{1}.postmodel.datadisplay.pntdata={'Hrad'}; gui.flmodel{1}.postmodel.datadisplay.pntlocation='element'; gui.flmodel{1}.postmodel.datadisplay.pntlagorder='2'; gui.flmodel{1}.postmodel.datadisplay.bnddata={'Hrad'}; gui.flmodel{1}.postmodel.datadisplay.bndcont='on'; gui.flmodel{1}.postmodel.datadisplay.bndlocation='element'; gui.flmodel{1}.postmodel.datadisplay.bndlagorder='2'; gui.flmodel{1}.postmodel.datadisplay.subdata={'Hrad'}; gui.flmodel{1}.postmodel.datadisplay.subcont='on'; gui.flmodel{1}.postmodel.datadisplay.subxspacing='10'; gui.flmodel{1}.postmodel.datadisplay.subxvectorspacing=''; gui.flmodel{1}.postmodel.datadisplay.subxisvector='off'; gui.flmodel{1}.postmodel.datadisplay.subyspacing='10'; gui.flmodel{1}.postmodel.datadisplay.subyvectorspacing=''; gui.flmodel{1}.postmodel.datadisplay.subyisvector='off'; gui.flmodel{1}.postmodel.datadisplay.sublocation='element'; gui.flmodel{1}.postmodel.datadisplay.sublagorder='2'; gui.flmodel{1}.postmodel.datadisplay.phase='0'; gui.flmodel{1}.postmodel.datadisplay.solnum='0'; gui.flmodel{1}.postmodel.datadisplay.selectvia='stored'; gui.flmodel{1}.postmodel.datadisplay.exportformat='ptd'; gui.flmodel{1}.postmodel.datadisplay.exportedim='2'; gui.flmodel{1}.postmodel.datadisplay.struct='off'; gui.flmodel{1}.postmodel.datadisplay.fullprecision='off'; gui.flmodel{1}.postmodel.datadisplay.interpdata={'Hrad'}; gui.flmodel{1}.postmodel.datadisplay.coord={'0','0'}; gui.flmodel{1}.geommodel.suppressed{1}=[]; gui.flmodel{1}.geommodel.suppressed{2}=[]; gui.flmodel{1}.geommodel.suppressed{3}=[]; gui.flmodel{1}.workplane.type='0'; gui.flmodel{1}.workplane.wrkpln='0,1,0,0,0,1,0,0,0'; gui.flmodel{1}.workplane.localsys='0,1,0,0,0,0,1,0,0,0,0,1'; gui.flmodel{1}.workplane.model2d='Geom1'; gui.flmodel{1}.workplane.quicktype='10'; gui.flmodel{1}.workplane.parameter='0'; gui.flmodel{1}.workplane.zdir='up'; gui.flmodel{1}.meshmodel.meshplot.subplot='on'; gui.flmodel{1}.meshmodel.meshplot.meshsubuseexpression='off'; gui.flmodel{1}.meshmodel.meshplot.meshsubcolor='128,128,128'; gui.flmodel{1}.meshmodel.meshplot.meshsubbordercheck='off'; gui.flmodel{1}.meshmodel.meshplot.meshwiresubplot='on'; gui.flmodel{1}.meshmodel.meshplot.meshwiresubcolor='192,192,192'; gui.flmodel{1}.meshmodel.meshplot.bndplot='on'; gui.flmodel{1}.meshmodel.meshplot.meshbndcolor='0,0,0'; gui.flmodel{1}.meshmodel.meshplot.useellogic='off'; gui.flmodel{1}.meshmodel.meshplot.ellogic=''; gui.flmodel{1}.meshmodel.meshplot.ellogictype='all'; gui.flmodel{1}.meshmodel.meshplot.meshkeepfraction='1'; gui.flmodel{1}.meshmodel.meshplot.meshkeeptype='random'; gui.flmodel{1}.meshmodel.meshplot.meshmap='jet'; gui.flmodel{1}.meshmodel.meshplot.meshmapdepth='1024'; gui.flmodel{1}.meshmodel.meshplot.meshbar='on'; uq~ txfemsrcom.femlab.geom.Geom2Vc/Oxrcom.femlab.geom.Geom͹6{L geomAssoctLcom/femlab/geom/GeomAssoc;Lversionq~xpwsq~wt COMSOL 3.2twt $Name: $t$Date: 2005/10/24 07:30:19 $xwluq~YlGeom2|=-C6??pԚ??8A?T??pԚ?T??8A????? 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AssocAttrib VectorInt AssocAttrib VectorInt/Ixwxsrcom.femlab.api.client.MFileInfo3$$LfemNameq~[historyq~[ storedNamesq~Lversionq~xpwuq~ tfem0tfem1uq~ )t`% COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flclear fem % COMSOL version clear vrsn vrsn.name = 'COMSOL 3.2'; vrsn.ext = ''; vrsn.major = 0; vrsn.build = 224; vrsn.rcs = '$Name: $'; vrsn.date = '$Date: 2005/10/24 07:30:19 $'; fem.version = vrsn; flbinaryfile=''; % Geometry g1=flbinary('g1','draw',flbinaryfile); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','2', ... 'M','9', ... 'eperp0','1.00', ... 'epara0','1.00', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','2', ... 'epara4','9', ... 'eperp5','9.407', ... 'epara5','11.62', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','9', ... 'eperp0','1.00', ... 'epara0','1.00', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','2', ... 'epara4','9', ... 'eperp5','9.407', ... 'epara5','11.62', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','9', ... 'eperp0','1.00', ... 'epara0','1.00', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','2', ... 'epara4','9', ... 'eperp5','9.407', ... 'epara5','11.62', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Geometry clear s s.objs={g1}; s.name={'R1'}; s.tags={'g1'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgelem',{1,[40],2,[20]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgelem',{1,[40],2,[20]}); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','0', ... 'eperp0','1.00', ... 'epara0','1.00', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','2', ... 'epara4','9', ... 'eperp5','9.407', ... 'epara5','11.62', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','0', ... 'eperp0','1.00', ... 'epara0','1.00', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','2', ... 'epara4','9', ... 'eperp5','9.407', ... 'epara5','11.62', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; prop.frame='xy'; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'}}; bnd.name = {'tangential_H'}; bnd.ind = [1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1}; equ.constr = {{'0';'0';'0'}}; equ.cporder = {{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'}}; equ.name = {'dielectric0:vacuum'}; equ.ind = [1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {}; % Functions clear fcns fem.functions = {}; % Descriptions clear descr descr.const= {'eperp2','eperp for the 2nd dielectric','eperp_293K_sapph','nominal room temperature values for same','c','speed of light (exact!)','epara0','ditto but now parallel to cylindrical axis','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','epara1','ditto but parallel to cylindrical axis','eperp3','etc.','epara2','epara for the 2nd dielectric','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of 1st dielectric perpendicular to cylindrical axis','eperp0','relative permittivity of vacuum perpendicular to cylindrical axis','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Hrad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=2.701017e10 Surface: Hrad', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.010881225026045,0.0235912252615741,-0.0139699998311698,0.0139699998311698,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Hrad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=5.901426e9 Surface: Hrad', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0157563611263049,-0.0141301144424153,0.0139699998311698,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Hazi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=5.901426e9 Surface: Hazi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0157563611263049,-0.0149179681136374,0.0147578535023919,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Haxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=5.901426e9 Surface: Haxi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0157563611263049,-0.0149179681136374,0.0147578535023919,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','5', ... 'eperp0','1.00', ... 'epara0','1.00', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','2', ... 'epara4','9', ... 'eperp5','9.407', ... 'epara5','11.62', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','5', ... 'eperp0','1.00', ... 'epara0','1.00', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','2', ... 'epara4','9', ... 'eperp5','9.407', ... 'epara5','11.62', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; prop.frame='xy'; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'}}; bnd.name = {'tangential_H'}; bnd.ind = [1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1}; equ.constr = {{'0';'0';'0'}}; equ.cporder = {{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'}}; equ.name = {'dielectric0:vacuum'}; equ.ind = [1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {}; % Functions clear fcns fem.functions = {}; % Descriptions clear descr descr.const= {'eperp2','eperp for the 2nd dielectric','eperp_293K_sapph','nominal room temperature values for same','c','speed of light (exact!)','epara0','ditto but now parallel to cylindrical axis','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','epara1','ditto but parallel to cylindrical axis','eperp3','etc.','epara2','epara for the 2nd dielectric','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of 1st dielectric perpendicular to cylindrical axis','eperp0','relative permittivity of vacuum perpendicular to cylindrical axis','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Haxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=4.124785e10 Surface: Haxi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0157563611263049,-0.0149179681136374,0.0147578535023919,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; prop.frame='xy'; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'}}; bnd.name = {'tangential_H'}; bnd.ind = [1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x'}; % Functions clear fcns fem.functions = {}; % Descriptions clear descr descr.const= {'eperp2','eperp for the 2nd dielectric','eperp_293K_sapph','nominal room temperature values for same','c','speed of light (exact!)','epara0','ditto but now parallel to cylindrical axis','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','epara1','ditto but parallel to cylindrical axis','eperp3','etc.','epara2','epara for the 2nd dielectric','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of 1st dielectric perpendicular to cylindrical axis','eperp0','relative permittivity of vacuum perpendicular to cylindrical axis','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Geometry [g2]=geomcopy({g1}); clear g1 g3=flbinary('g3','draw',flbinaryfile); g4=flbinary('g4','draw',flbinaryfile); g5=flbinary('g5','draw',flbinaryfile); g6=flbinary('g6','draw',flbinaryfile); g7=flbinary('g7','draw',flbinaryfile); g8=flbinary('g8','draw',flbinaryfile); clear s s.objs={g3,g4,g5,g6,g7,g8}; s.name={'R1','R2','R3','R4','R5','R6'}; s.tags={'g3','g4','g5','g6','g7','g8'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgelem',{8,[15],12,[15],13,[20],16,[30],17,[20],18,[20],19,[20]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgelem',{8,[15],12,[15],13,[24],16,[30],17,[20],18,[20],19,[20]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgelem',{8,[20],12,[15],13,[24],16,[30],17,[20],18,[20],19,[20]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgelem',{8,[18],12,[15],13,[24],16,[30],17,[20],18,[20],19,[20]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgelem',{8,[18],12,[15],13,[24],16,[30],17,[20],18,[20],19,[20]}); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','5', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','2', ... 'epara4','9', ... 'eperp5','9.407', ... 'epara5','11.62', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','5', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,2,2,2,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,2,1,1,2,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x'}; % Functions clear fcns fem.functions = {}; % Descriptions clear descr descr.const= {'epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','fc','constant used internally --do not modify','c','speed of light (exact!)','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Haxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=2.272202e11 Surface: Haxi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0179127983008426,0.0403164999692663,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','9', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','9', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,2,2,2,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,2,1,1,2,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x'}; % Functions clear fcns fem.functions = {}; % Descriptions clear descr descr.const= {'epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','fc','constant used internally --do not modify','c','speed of light (exact!)','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Haxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.686226e10 Surface: Haxi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0218126933194372,0.044216394987861,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Haxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: Haxi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0218126933194372,0.044216394987861,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Haxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: Haxi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0218126933194372,0.044216394987861,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Hrad*Hrad+Hazi*Hazi+Haxi*Haxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: Hrad*Hrad+Hazi*Hazi+Haxi*Haxi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0218126933194372,0.044216394987861,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Hrad*Hrad+Hazi*Hazi+Haxi*Haxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: Hrad*Hrad+Hazi*Hazi+Haxi*Haxi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0231882993258393,0.045592000994263,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi)', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0231882993258393,0.045592000994263,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','9', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'spf','1e-6'}; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+0.00001)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+0.00001)', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0225630238683838,0.0449667255368076,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+0.0001)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+0.0001)', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0221087878858377,0.0445124895542614,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+0.000001)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+0.000001)', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0221087878858377,0.0445124895542614,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0221087878858377,0.0445124895542614,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0221087878858377,0.0445124895542614,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0221087878858377,0.0445124895542614,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0221087878858377,0.0445124895542614,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00233658994443658,0.0399897487140879,-0.0274195297985001,0.0498232314669239,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,0.0398949969370733,-0.00785416306104278,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,0.0398949969370733,-0.00785416306104278,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',0.5, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,t`0.0398949969370733,-0.00785416306104278,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,0.0398949969370733,-0.00785416306104278,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,0.0398949969370733,-0.00785416306104278,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,0.0398949969370733,-0.00785416306104278,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,0.0398949969370733,-0.00785416306104278,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',19, ... 'phase',(0)*pi/180, ... 'title','lambda(19)=1.02501e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,0.0440877290624526,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',18, ... 'phase',(0)*pi/180, ... 'title','lambda(18)=1.140409e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,0.0440877290624526,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',17, ... 'phase',(0)*pi/180, ... 'title','lambda(17)=1.233746e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,0.0440877290624526,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',16, ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.239518e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00179499985679286,0.0440877290624526,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0018741080101019,0.0441668372157617,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0018741080101019,0.0441668372157617,-0.00856613644082418,0.0428541632100544,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','9', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'spf','1e-6'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.00', ... 'M','9', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'spf','1e-6'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','9', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'spf','1e-6'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','9', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'spf','1e-6'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,2,2,2,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,2,1,1,2,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','spf','small postivie finite number (to avoid close-to-zero values)','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.759825e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00229999844552669,0.0445927276511865,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.759825e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00229999844552669,0.0445927276511865,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.593191e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00229999844552669,0.0445927276511865,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294742e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00229999844552669,0.0445927276511865,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294742e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00229999844552669,0.0445927276511865,-0.00856613644082418,0.0428541632100544,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'spf','1e-6'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'spf','1e-6'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,2,2,2,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,2,1,1,2,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','spf','small postivie finite number (to avoid close-to-zero values)','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.686226e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00229999844552669,0.0445927276511865,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.344946e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00229999844552669,0.0445927276511865,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.366096e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00229999844552669,0.0445927276511865,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00238084797327964,0.0446735771789394,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',19, ... 'phase',(0)*pi/180, ... 'title','lambda(19)=1.02501e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00238084797327964,0.0446735771789394,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',18, ... 'phase',(0)*pi/180, ... 'title','lambda(18)=1.140409e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00238084797327964,0.0446735771789394,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',16, ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.239518e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00238084797327964,0.0446735771789394,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',18, ... 'phase',(0)*pi/180, ... 'title','lambda(18)=1.140409e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00238084797327964,0.0446735771789394,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',19, ... 'phase',(0)*pi/180, ... 'title','lambda(19)=1.02501e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00238084797327964,0.0446735771789394,-0.00856613644082418,0.0428541632100544,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.294123e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00238084797327964,0.0446735771789394,-0.00856613644082419,0.0428541632100544,-1,1]); % Geometry [g9,g10,g11,g12,g13,g14]=geomcopy({g3,g4,g5,g6,g7,g8}); clear g3 g4 g5 g6 g7 g8 g15=flbinary('g15','draw',flbinaryfile); g16=flbinary('g16','draw',flbinaryfile); g17=flbinary('g17','draw',flbinaryfile); g18=flbinary('g18','draw',flbinaryfile); g19=flbinary('g19','draw',flbinaryfile); g20=flbinary('g20','draw',flbinaryfile); g21=flbinary('g21','draw',flbinaryfile); g22=flbinary('g22','draw',flbinaryfile); g23=flbinary('g23','draw',flbinaryfile); g24=flbinary('g24','draw',flbinaryfile); g25=flbinary('g25','draw',flbinaryfile); g26=flbinary('g26','draw',flbinaryfile); g27=flbinary('g27','draw',flbinaryfile); g28=flbinary('g28','draw',flbinaryfile); g29=flbinary('g29','draw',flbinaryfile); g30=flbinary('g30','draw',flbinaryfile); g31=flbinary('g31','draw',flbinaryfile); g32=flbinary('g32','draw',flbinaryfile); g33=flbinary('g33','draw',flbinaryfile); g34=flbinary('g34','draw',flbinaryfile); g35=flbinary('g35','draw',flbinaryfile); g36=flbinary('g36','draw',flbinaryfile); g37=flbinary('g37','draw',flbinaryfile); g38=flbinary('g38','draw',flbinaryfile); g39=flbinary('g39','draw',flbinaryfile); g40=flbinary('g40','draw',flbinaryfile); g41=flbinary('g41','draw',flbinaryfile); clear s s.objs={g15,g16,g17,g18,g19,g20,g21,g22,g23,g24,g25,g26,g27,g28,g29, ... g30,g31,g32,g33,g34,g35,g36,g37,g38,g39,g40,g41}; s.name={'s1a1','s1b1','s1','s2','s3','s4','s5','v1','v8a1','v8b1', ... 'v9a1','v9b1','v10a1','v10b1','v10c1','v11a1','v11b1','v11c1','v2','v3', ... 'v4','v5','v6','v7','v8','v9','v10'}; s.tags={'g15','g16','g17','g18','g19','g20','g21','g22','g23','g24', ... 'g25','g26','g27','g28','g29','g30','g31','g32','g33','g34','g35','g36', ... 'g37','g38','g39','g40','g41'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgelem',{2,[7],5,[4],6,[10],10,[4],13,[2],20,[6],27,[8],34,[10],38,[16],40,[7],41,[16],51,[26],59,[40],67,[26],68,[3],69,[7],71,[7],72,[3],73,[26]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgelem',{2,[7],5,[4],6,[10],10,[4],13,[2],20,[6],27,[7],34,[10],38,[16],40,[7],41,[16],51,[26],59,[40],67,[26],68,[3],69,[7],71,[7],72,[3],73,[26]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgelem',{2,[7],5,[4],6,[10],10,[4],13,[2],20,[6],27,[8],34,[10],38,[16],40,[7],41,[16],51,[26],59,[40],67,[26],68,[3],69,[7],71,[7],72,[3],73,[26]}); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dit`electric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','spf','small postivie finite number (to avoid close-to-zero values)','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'eperp1','9.407', ... 'epara1','11.62', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'spf','1e-6'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','spf','small postivie finite number (to avoid close-to-zero values)','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.274361e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0291797175750504,0.0291899732992421,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',18, ... 'phase',(0)*pi/180, ... 'title','lambda(18)=9.144314e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.035498760448906,0.0355090161730977,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.287051e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0356203491075053,0.035630604831697,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.801924e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0356203491075053,0.035630604831697,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',19, ... 'phase',(0)*pi/180, ... 'title','lambda(19)=8.643685e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0356203491075053,0.035630604831697,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',18, ... 'phase',(0)*pi/180, ... 'title','lambda(18)=9.208728e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0356203491075053,0.035630604831697,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.801924e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0356203491075053,0.035630604831697,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.326233e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.80211e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.326497e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.801554e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','29979245t`8', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=2.202673e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=2.202673e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0351068437078331,0.0351170994320248,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.801184e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0351068437078331,0.0351170994320248,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.286256e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.794991e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.055352e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=5.762968e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.146114e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=5.763133e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','7', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*t`test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.120027e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.01791e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=6.443297e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.220922e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.123376e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','10', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.354009e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=8.47851e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.376963e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=8.47851e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','12', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','12', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','12', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.54642e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.825549e9 t` Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.616243e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.049614e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','14', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','14', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.678853e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.116492e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','15', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','15', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.741669e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.1832e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','16', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=2.367326e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.249751e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0351068437078331,0.0351170994320248,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)t`+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.054965e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=5.76203e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','7', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.11972e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=6.442435e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.221754e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.122579e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.326513e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.801184e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','10', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.375851e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=8.477818e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-et`perp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=3.254938e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.152388e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0351068437078331,0.0351170994320248,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','12', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.54642e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.824937e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=2.206405e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.049556e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0351068437078331,0.0351170994320248,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','14', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.735268e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.116437e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','15', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=3.290388e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.183148e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0351068437078331,0.0351170994320248,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','16', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','16', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... t` 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','15', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','16', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.849894e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.249701e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.054726e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=5.7583e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','7', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=2.108758e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=6.43786e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.252493e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.117184e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','10', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.framt`e = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.353087e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=8.470846e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.471293e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.144653e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','12', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.54642e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=9.816451e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','12', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.655171e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.048633e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0348655243155999,0.0348757800397916,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','14', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.678244e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.115441e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','15', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazit`x)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=3.374604e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.18208e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0351068437078331,0.0351170994320248,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','16', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','1*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.80451e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.248562e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','16', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.80561e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=1.249818e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.326233e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.80211e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0104489449066157,0.0533709279469029,-0.0349857679437989,0.0349960236679905,-1,1]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','t`relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.472172e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0153345923215852,0.0582565753618724,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.287051e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',16, ... 'phase',(0)*pi/180, ... 'title','lambda(16)=9.83803e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(20)=7.801924e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',19, ... 'phase',(0)*pi/180, ... 'title','lambda(19)=8.643685e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',18, ... 'phase',(0)*pi/180, ... 'title','lambda(18)=9.208728e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',17, ... 'phase',(0)*pi/180, ... 'title','lambda(17)=9.74777e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',16, ... 'phase',(0)*pi/180, ... 'title','lambda(16)=9.83803e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',16, ... 'phase',(0)*pi/180, ... 'title','lambda(16)=9.83803e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.458182e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',19, ... 'phase',(0)*pi/180, ... 'title','lambda(19)=9.909482e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',19, ... 'phase',(0)*pi/180, ... 'title','lambda(19)=9.909482e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',19, ... 'phase',(0)*pi/180, ... 'title','lambda(19)=9.909482e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2738*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3501*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2738', ... 'epara_4K_sapph_NPL','11.3501'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2738*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3501*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2738', ... 'epara_4K_sapph_NPL','11.3501'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2738*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3501*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2738', ... 'epara_4K_sapph_NPL','11.3501'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2738*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3501*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2738', ... 'epara_4K_sapph_NPL','11.3501'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.221787e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2738*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3501*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2738', ... 'epara_4K_sapph_NPL','11.3501'}; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.221787e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2738*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3501*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.221787e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','t`shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',20, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.251868e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.251868e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0349857679437989,0.0349960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',18, ... 'phase',(0)*pi/180, ... 'title','lambda(18)=8.44837e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',17, ... 'phase',(0)*pi/180, ... 'title','lambda(17)=9.037046e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=9.422262e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=9.800158e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=9.422262e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',16, ... 'phase',(0)*pi/180, ... 'title','lambda(16)=9.225876e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=9.422262e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=9.800158e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=9.422262e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',16, ... 'phase',(0)*pi/180, ... 'title','lambda(16)=9.225876e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',17, ... 'phase',(0)*pi/180, ... 'title','lambda(17)=9.037046e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=9.800158e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.027374e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.143696e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.016726e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','7', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axt`is','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.338821e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.228098e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','10', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.228098e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.31608e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.399235e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','12', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.472839e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielect`tric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.565884e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','14', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','14', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.633227e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','15', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.702893e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','16', ... 'delta_eperp1','0*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.749051e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','1*2e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*2e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.016726e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','7', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_st`apph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.083872e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.143252e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.228098e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','10', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.315602e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.398693e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','12', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.472231e10 Surface: log10(Hrad*Hradt`+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.559638e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','14', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.624103e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','15', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','15', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.686176e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','14', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.624103e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','16', ... 'delta_eperp1','1*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.748442e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407't`, ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.182392e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','7', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.35825e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','8', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.143582e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.228098e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.315915e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','11', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*t`test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.399101e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','12', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.472733e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','13', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.547421e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','14', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.624299e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','15', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.686511e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','16', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','1*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)t`*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.748789e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1.0', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.049303e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','11', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.399505e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','16', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10.0', ... 'M','16', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.749286e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.018311e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=8.358121e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=8.845164e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,2t`7]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','7', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','7', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.084299e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=6.438555e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=7.389506e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=7.695231e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=8.312546e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=8.623541e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=8.751501e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=9.112091e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=9.557666e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=9.632117e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=9.917532e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',6, ... 'phase',(0)*pi/180, ... 'title','lambda(6)=9.986376e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',5, ... 'phase',(0)*pi/180, ... 'title','lambda(5)=1.016923e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',4, ... 'phase',(0)*pi/180, ... 'title','lambda(4)=1.017251e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',3, ... 'phase',(0)*pi/180, ... 'title','lambda(3)=1.031561e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',2, ... 'phase',(0)*pi/180, ... 'title','lambda(2)=1.066226e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',6, ... 'phase',(0)*pi/180, ... 'title','lambda(6)=9.986376e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=9.917532e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.084299e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','7', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.084299e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=9.557666e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=9.917532e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',6, ... 'phase',(0)*pi/180, ... 'title','lambda(6)=9.986376e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','8', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','8', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3t`', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','8', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.182787e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','8', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.182787e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.143696e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.435251e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.228098e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',2, ... 'phase',(0)*pi/180, ... 'title','lambda(2)=1.22783e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',3, ... 'phase',(0)*pi/180, ... 'title','lambda(3)=1.214784e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',4, ... 'phase',(0)*pi/180, ... 'title','lambda(4)=1.204933e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',5, ... 'phase',(0)*pi/180, ... 'title','lambda(5)=1.193498e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',2, ... 'phase',(0)*pi/180, ... 'title','lambda(2)=1.22783e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',3, ... 'phase',(0)*pi/180, ... 'title','lambda(3)=1.214784e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',4, ... 'phase',(0)*pi/180, ... 'title','lambda(4)=1.204933e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','7', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','7', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','7', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxt`i*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.118128e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.34275e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.31608e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',2, ... 'phase',(0)*pi/180, ... 'title','lambda(2)=1.312683e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',3, ... 'phase',(0)*pi/180, ... 'title','lambda(3)=1.311544e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','12', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','12', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','12', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.472839e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','13', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','13', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','13', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'t`0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.559863e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','12', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','12', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.473139e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','13', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.547829e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','14', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.622899e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','10', ... 'M','15', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.686999e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','16', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','16', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.686999e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.686999e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.182362e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.245863e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.338786e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.368061e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.015992606629861,0.0589145896701482,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.413811e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlet`vels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.476622e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.512414e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.534592e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.512414e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.476622e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.512414e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.476622e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.413811e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.368061e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.338786e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.245863e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.182362e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.245863e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0590172022678194,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.338786e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.368061e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.413811e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.182362e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.245863e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.338786e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.368061e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.413811e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.476622e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.512414e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.534592e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.512414e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.476622e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.413811e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.368061e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.338786e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.245863e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.182362e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.338786e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.534592e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.512414e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)t`','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.534592e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.476622e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.413811e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.368061e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.368061e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.368061e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.338786e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.245863e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.182362e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.182362e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.245863e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.338786e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.368061e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.476622e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.534592e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.512414e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.476622e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442533e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439452e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.413811e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.368061e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.338786e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.245863e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.182362e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','16', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.749051e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0160952192275322,0.0580936888887782,-0.0324857679437989,0.0374960236679905,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.248806e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.309936e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.400127e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.441772e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.485793e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.502893e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.509431e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.545196e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.579882e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... t` 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.597478e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','6', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=2.009831e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=5.758766e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0395464618597006,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=6.76759e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=6.954213e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.0149903200408515,0.0200005757650432,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=7.586843e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.015049828367052,0.0200600840912437,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=7.96432e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.015049828367052,0.0200600840912437,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=8.172575e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.015049828367052,0.0200600840912437,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=8.358121e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.015049828367052,0.0200600840912437,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=8.431681e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=8.747063e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=8.431681e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=8.358121e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=8.172575e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00245200780154536,0.0327227241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=7.96432e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=7.586843e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=6.954213e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=6.76759e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=5.758766e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','7', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.084299e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=6.438555e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=7.389506e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=7.695231e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=8.312546e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=8.623541e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=8.751501e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=9.112091e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=9.557666e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=9.632117e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','8', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradxt`)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.143696e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=7.118099e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=7.118099e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=8.011071e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=8.44837e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=9.037046e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=9.225876e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=9.422262e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=9.800158e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.027374e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.069285e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.074943e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',6, ... 'phase',(0)*pi/180, ... 'title','lambda(6)=1.080404e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.228098e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=7.796116e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=8.637439e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=9.202806e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=9.741057e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=9.831303e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.013015e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.049154e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.091479e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.124872e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','10', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.31608e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=8.472173e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=9.268148e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=9.955611e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.036514e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.052099e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... t` 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.084476e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.118239e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.154596e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.183813e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.210097e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','11', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.399235e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=9.146177e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=9.902224e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.070585e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.096324e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.12425e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.155943e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.186806e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.216465e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.246274e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.275527e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','12', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','12', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','12', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.490902e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=9.818166e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.053882e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.145331e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.15633e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.145331e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.15633e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.196701e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.227207e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.254082e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.278379e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.311262e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.340935e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','13', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^t`2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.565884e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.048824e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.117728e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.216749e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.219806e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.269129e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.298195e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.319017e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.342203e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.377635e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.406051e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',6, ... 'phase',(0)*pi/180, ... 'title','lambda(6)=1.491113e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.633227e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.11565e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.18171e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.277558e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.294027e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.341466e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.368889e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.381442e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',9, ... 'phase',(0)*pi/180, ... 'title','lambda(9)=1.408552e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',8, ... 'phase',(0)*pi/180, ... 'title','lambda(8)=1.444716e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.470626e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',6, ... 'phase',(0)*pi/180, ... 'title','lambda(6)=1.513576e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','15', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.686764e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.182307e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.245789e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0t`.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.338702e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',11, ... 'phase',(0)*pi/180, ... 'title','lambda(11)=1.439296e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',10, ... 'phase',(0)*pi/180, ... 'title','lambda(10)=1.442425e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','16', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.749051e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.248806e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.309936e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.400127e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.441772e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.485793e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2848*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3660*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.228098e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',7, ... 'phase',(0)*pi/180, ... 'title','lambda(7)=1.14494e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',6, ... 'phase',(0)*pi/180, ... 'title','lambda(6)=1.180524e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',5, ... 'phase',(0)*pi/180, ... 'title','lambda(5)=1.193498e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',4, ... 'phase',(0)*pi/180, ... 'title','lambda(4)=1.204933e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.228098e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=9.202806e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[0.00620200780154536,0.0364727241145628,-0.0151097428934314,0.020119998617623,-1,1]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'-(Haziy*M*test(Haxi))+Hazix*test(Hazi)+Hazi*test(Hazix)-Hrad*M*test(Hazix)-Haxi*M*test(Haziy)-Hazix*M*test(Hrad)+(Haxi*M^2*test(Haxi)+(Hazi-Hrad*M)*(test(Hazi)-M*test(Hrad)))/x+x*((Haxix-Hrady)*test(Haxix)+Hazix*test(Hazix)+Haziy*test(Haziy)-Haxix*test(Hrady)+Hrady*test(Hrady))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara1*Haziy*M*test(Haxi)+eperp1*Hazix*test(Hazi)+eperp1*Hazi*test(Hazix)-eperp1*Hrad*M*test(Hazix)-epara1*Haxi*M*test(Haziy)-eperp1*Hazix*M*test(Hrad))/(epara1*eperp1)+(epara1*Haxi*M^2*test(Haxi)+eperp1*Hazi*test(Hazi)-eperp1*Hrad*M*test(Hazi)-eperp1*Hazi*M*test(Hrad)+eperp1*Hrad*M^2*test(Hrad))/(epara1*eperp1*x)+(x*(epara1*(Haxix-Hrady)*test(Haxix)+eperp1*Hazix*test(Hazix)+epara1*Haziy*test(Haziy)-epara1*Haxix*test(Hrady)+epara1*Hrady*test(Hrady)))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.228098e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00893335035496t`334,0.0516080822710715,-0.0327858550315698,0.0377961107557615,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1, ... 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2, ... 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,2,2, ... 2,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_0:vacuum','dielectric_1','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.228098e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00893335035496334,0.0516080822710715,-0.0327858550315698,0.0377961107557615,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=9.202806e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00893335035496334,0.0516080822710715,-0.0418314245107177,0.0468416802349093,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=9.202806e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00893335035496334,0.0516080822710715,-0.0327858550315698,0.0377961107557615,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=9.202806e9 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',2, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00893335035496334,0.0516080822710715,-0.0327858550315698,0.0377961107557615,-1,1]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Geometry [g2,g9,g10,g11,g12,g13,g14,g42,g43,g44,g45,g46,g47,g48,g49,g50,g51,g52,g53,g54,g55,g56,g57,g58,g59,g60,g61]=geomcopy({g28,g38,g27,g16,g20,g35,g22,g33,g19,g30,g23,g25,g32,g40,g31,g17,g21,g39,g18,g34,g29,g24,g41,g36,g37,g15,g26}); clear g28 g38 g27 g16 g20 g35 g22 g33 g19 g30 g23 g25 g32 g40 g31 g17 g21 g39 g18 g34 g29 g24 g41 g36 g37 g15 g26 g62=flbinary('g62','draw',flbinaryfile); g63=flbinary('g63','draw',flbinaryfile); g64=flbinary('g64','draw',flbinaryfile); g65=flbinary('g65','draw',flbinaryfile); g66=flbinary('g66','draw',flbinaryfile); g67=flbinary('g67','draw',flbinaryfile); g68=flbinary('g68','draw',flbinaryfile); g69=flbinary('g69','draw',flbinaryfile); g70=flbinary('g70','draw',flbinaryfile); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','9', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Geometry clear s s.objs={g62,g63,g64,g65,g66,g67,g68,g69,g70}; s.name={'s1','s2','s3','s4','v1','v2','v3','v4','v5'}; s.tags={'g62','g63','g64','g65','g66','g67','g68','g69','g70'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Initialize mesh fem.mesh=meshinit(fem, ... 'hmax',[], ... 'hmaxfact',1, ... 'hgrad',1.3, ... 'hcurve',0.3, ... 'hcutoff',0.001, ... 'hnarrow',1, ... 'hpnt',10, ... 'xscale',1.0, ... 'yscale',1.0, ... 'mlevel','sub'); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.654084e11 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0190790298376714,0.0617537617537796,-0.0227182521147096,0.0715203062267194,-1,1]); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[6],3,[30],5,[8],7,[6],14,[20],21,[24]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[10],3,[30],5,[14],7,[6],14,[20],21,[24]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[10],3,[30],5,[14],7,[10],14,[20],21,[24]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[10],3,[30],5,[14],7,[10],14,[20],21,[24]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[12],3,[30],5,[14],7,[10],14,[20],21,[24]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[11],3,[30],5,[14],7,[10],14,[20],21,[24]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[11],3,[30],5,[14],7,[10],14,[20],21,[24]}); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi'}; % Descriptions clear descr descr.expr= {'MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0190790298376714,0.0617537617537796,-0.0227182521147096,0.0715203062267194,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0190790298376714,0.0617537617537796,-0.0347955783492975,0.0835976324613074,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030399e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6) Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Hazi-Hrad*M+Hazix*x','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Hazi-Hrad*M+Hazix*x Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00112800835940596,0.0507685982271237,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'2.0','1.00'}, ... 'epara',{'2.0','1.00'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','0', ... 'Eazi','0', ... 'Eaxi','0'}; % Descriptions clear descr descr.expr= {'Eaxi','axiall component of electric field strength','MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'init',fem0.sol, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'eperp','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: eperp Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00193862774883241,0.0515792176165501,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'eperp','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: eperp Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00112800835940596,0.0507685982271237,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(ept`ara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1.00'}, ... 'epara',{'epara1','1.00'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','0', ... 'Eazi','0', ... 'Eaxi','0'}; % Descriptions clear descr descr.expr= {'Eaxi','axiall component of electric field strength','MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'init',fem0.sol, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'eperp','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: eperp Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'(Hazi-Hrad*M+Hazix*x)/epara','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: (Hazi-Hrad*M+Hazix*x)/epara Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'(Hazi-Hrad*M+Hazix*x)/epara','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: (Hazi-Hrad*M+Hazix*x)/epara Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00163454908198365,0.0512751389497014,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Drad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Drad Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Daxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Daxi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00246126295747873,0.0521018528251965,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'MagEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: MagEn Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00214526035642077,0.0517858502241385,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Erad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Erad Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00183649445615039,0.0514770843238681,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eaxi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eazi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eazi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Erad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Erad Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1.00'}, ... 'epara',{'epara1','1.00'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','Haxi*M- Haziy*x/eperp', ... 'Eazi','-Haxix+Hrady/eperp', ... 'Eaxi','Hazi-Hrad*M+Hazix*x/epara'}; % Descriptions clear descr descr.expr= {'Eaxi','axiall component of electric field strength','MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'init',fem0.sol, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Erad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: Erad Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: Eaxi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00224977801258464,0.0518903678803024,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eaxi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00214526035642077,0.0517858502241385,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1.00'}, ... 'epara',{'epara1','1.00'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','Haxi*M- Haziy*x/eperp', ... 'Eazi','-Haxix+Hrady/eperp', ... 'Eaxi','Hazi-Hrad*M+Hazix*x/epara', ... 'ElecEn','log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-06)'}; % Descriptions clear descr descr.expr= {'Eaxi','axiall component of electric field strength','MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)','ElecEn','electric field energy density','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'init',fem0.sol, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Eaxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.513625e10 Surface: Eaxi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eaxi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00224977801258464,0.0518903678803024,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00214526035642077,0.0517858502241385,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1.00'}, ... 'epara',{'epara1','1.00'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','(Haxi*M- Haziy*x)/eperp', ... 'Eazi','(-Haxix+Hrady)/eperp', ... 'Eaxi','(Hazi-Hrad*M+Hazix*x)/epara', ... 'ElecEn','log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-06)'}; % Descriptions clear descr descr.expr= {'Eaxi','axiall component of electric field strength','MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)','ElecEn','electric field energy density','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'init',fem0.sol, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: ElecEn Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00163454908198365,0.0512751389497014,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eaxi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00163454908198365,0.0512751389497014,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Erad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Erad Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00163454908198365,0.0512751389497014,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eazi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eazi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00246126295747873,0.0521018528251965,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-t`M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1.00'}, ... 'epara',{'epara1','1.00'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','(Haxi*M- Haziy*x)/eperp', ... 'Eazi','(-Haxix+Hrady)/eperp', ... 'Eaxi','(Hazi-Hrad*M+Hazix*x)/epara', ... 'ElecEn','log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-06)', ... 'Emag','og10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-06)'}; % Descriptions clear descr descr.expr= {'Eaxi','axiall component of electric field strength','MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)','ElecEn','electric field energy density','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','Emag','electric field magnitude'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Eazi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: Eazi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00246126295747873,0.0521018528251965,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eazi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eazi Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00246126295747873,0.0521018528251965,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00246126295747873,0.0521018528251965,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Hazi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Hazi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00256824945901339,0.0522088393267311,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'ElecEn','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: ElecEn Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'ElecEn','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: ElecEn Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'ElecEn','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: ElecEn Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'ElecEn','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: ElecEn Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'ElecEn','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: ElecEn Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'MagEn','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: MagEn Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'MagEn','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030399e10 Surface: ElecEn Contour: MagEn Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'MagEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'MagEn','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030399e10 Surface: MagEn Contour: MagEn Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'MagEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.2,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030399e10 Surface: MagEn Contour: Haxi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'MagEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030399e10 Surface: MagEn Contour: Haxi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030399e10 Surface: ElecEn Contour: Haxi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.100904e10 Surface: ElecEn Contour: Haxi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','off'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',[], ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00325502154171962,0.0483829640817542,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'lindata',{'Hrad','cont','internal'}, ... 'linstyle','interp', ... 'linbar','on', ... 'linmap','jet(1024)', ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Boundary: Hrad Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'bdl',{[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]}, ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00574460143455437,0.0553851913022721,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00256824945901339,0.0522088393267311,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'tridlim',[0.001 10.00], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00256824945901339,0.0522088393267311,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'tridlim',[0.001 1000], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00214526035642077,0.0517858502241385,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'tridlim',[0.001 1000], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00214526035642077,0.0517858502241385,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'tridlim',[0.001 1000], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00214526035642077,0.0517858502241385,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'tridlim',[0.001 1000], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00214526035642077,0.0517858502241385,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1.00'}, ... 'epara',{'epara1','1.00'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','(Haxi*M- Haziy*x)/eperp', ... 'Eazi','(-Haxix+Hrady)/eperp', ... 'Eaxi','(Hazi-Hrad*M+Hazix*x)/epara', ... 'ElecEn','log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-06)', ... 'Emag','log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-04)'}; % Descriptions clear descr descr.expr= {'Eaxi','axiall component of electric field strength','MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)','ElecEn','electric field energy density','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','Emag','electric field magnitude'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'init',fem0.sol, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'tridlim',[0.001 1000], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00214526035642077,0.0517858502241385,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00214526035642077,0.0517858502241385,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00183649445615039,0.0514770843238681,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','flat', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00183649445615039,0.0514770843238681,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00183649445615039,0.0514770843238681,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','bone(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.0018t`3649445615039,0.0514770843238681,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00183649445615039,0.0514770843238681,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','pink(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00183649445615039,0.0514770843238681,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','hot(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00183649445615039,0.0514770843238681,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Emag','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Emag Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00183649445615039,0.0514770843238681,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00183649445615039,0.0514770843238681,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eaxi Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Erad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Erad Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00173513784250016,0.0513757277102179,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Drad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Drad Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00246126295747873,0.0521018528251965,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Erad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Erad Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00246126295747873,0.0521018528251965,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eazi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eazi Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00246126295747873,0.0521018528251965,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eazi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(90)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eazi Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00246126295747873,0.0521018528251965,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Erad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(90)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Erad Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.0040395349016057,0.0536801247693234,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Erad','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Erad Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.0040395349016057,0.0536801247693234,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eazi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: Eazi Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00267607837394595,0.0523166682416637,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00246126295747873,0.0521018528251965,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1.00'}, ... 'epara',{'epara1','1.00'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','(Haxi*M- Haziy*x)/eperp', ... 'Eazi','(-Haxix+Hrady)/eperp', ... 'Eaxi','(Hazi-Hrad*M+Hazix*x)/epara', ... 'ElecEn','log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-04)', ... 'Emag','log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-04)'}; % Descriptions clear descr descr.expr= {'Eaxi','axiall component of electric field strength','MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)','ElecEn','electric field energy density','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','Emag','electric field magnitude'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'init',fem0.sol, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495903e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00153471948192387,0.0511753093496416,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecEn','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: ElecEn Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00163454908198365,0.0512751389497014,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-04)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-04) Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-8.24805507925479E-4,0.0459527480479601,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'Haxi*Haxi','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: Haxi*Haxi Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-8.24805507925479E-4,0.0459527480479601,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'lo10(Haxi*Haxi)','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: lo10(Haxi*Haxi) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00121656912149901,0.0508571589892167,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'lo10(Haxi*Haxi+1e-04)','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: lo10(Haxi*Haxi+1e-04) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-6.38948398362847E-4,0.0457668909383974,-0.00182680812279646,0.0514673979905142,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-04)','cont','internal'}, ... 'contlevels',20, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-04) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00395997697685237,0.049087919516887,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-04)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-04) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-04)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.5, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-04) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-04)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-04) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-04)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-04) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-06), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-06)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-1)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-1)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Hat`xi+1e-1), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-1)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-1)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-1)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e-1), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e-1)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e1)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e1), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e1)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e1), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e1)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e1), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e1)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e1), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e1)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi*log10(Hazi*Hazi+Haxi*Haxi+1e1), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(Hazi*Hazi+Haxi*Haxi+1e01)*Hazi/(Hazi*Hazi+Haxi*Haxi)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(Hazi*Hazi+Haxi*Haxi+1e01)*Hazi/(Hazi*Hazi+Haxi*Haxi), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(Hazi*Hazi+Haxi*Haxi+1e01)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(Hazi*Hazi+Haxi*Haxi+1e01)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), Haxi*log10(Hazi*Hazi+Haxi*Haxi+1e1)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(Hazi*Hazi+Haxi*Haxi+1e01)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(Hazi*Hazi+Haxi*Haxi+1e01)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(Hazi*Hazi+Haxi*Haxi+1e01)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(Hazi*Hazi+Haxi*Haxi+1e01)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(Hazi*Hazi+Haxi*Haxi+1e-03)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(Hazi*Hazi+Haxi*Haxi+1e-03)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(Hazi*Hazi+Haxi*Haxi+1e-03)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(Hazi*Hazi+Haxi*Haxi+1e-03)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(Hazi*Hazi+Haxi*Haxi+1e-07)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(Hazi*Hazi+Haxi*Haxi+1e-07)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(Hazi*Hazi+Haxi*Haxi+1e-07)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(Hazi*Hazi+Haxi*Haxi+1e-07)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(Hazi*Hazi+Haxi*Haxi+1e+07)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(Hazi*Hazi+Haxi*Haxi+1e+07)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(Hazi*Hazi+Haxi*Haxi+1e+07)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(Hazi*Hazi+Haxi*Haxi+1e+07)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(Hazi*Hazi+Haxi*Haxi+1e-07)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(Hazi*Hazi+Haxi*Haxi+1e-07)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(Hazi*Hazi+Haxi*Haxi+1e-07)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(Hazi*Hazi+Haxi*Haxi+1e-07)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [log10(1)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), log10(1)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'(log10(Hazi*Hazi+Haxi*Haxi)+2)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','(log10(Hazi*Hazi+Haxi*Haxi)+2)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [(log10(Hazi*Hazi+Haxi*Haxi)+2)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), (log10(Hazi*Hazi+Haxi*Haxi)+2)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'(log10(Hazi*Hazi+Haxi*Haxi)+4)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','(log10(Hazi*Hazi+Haxi*Haxi)+4)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [(log10(Hazi*Hazi+Haxi*Haxi)+4)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), (log10(Hazi*Hazi+Haxi*Haxi)+4)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'(log10(Hazi*Hazi+Haxi*Haxi)+10)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','(log10(Hazi*Hazi+Haxi*Haxi)+10)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [(log10(Hazi*Hazi+Haxi*Haxi)+10)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), (log10(Hazi*Hazi+Haxi*Haxi)+10)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'(log10(Hazi*Hazi+Haxi*Haxi)+14)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi)','(log10(Hazi*Hazi+Haxi*Haxi)+14)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [(log10(Hazi*Hazi+Haxi*Haxi)+14)*Hazi/sqrt(Hazi*Hazi+Haxi*Haxi), (log10(Hazi*Hazi+Haxi*Haxi)+14)*Haxi/sqrt(Hazi*Hazi+Haxi*Haxi)]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192542e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-9.04630684642005E-4,0.0460325732246766,-0.00112800835940596,0.0507685982271237,-1,1]); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[17],3,[40],5,[20],7,[14],14,[28],21,[30]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[17],3,[40],5,[22],7,[14],14,[28],21,[30]}); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1.00'}, ... 'epara',{'epara1','1.00'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','(Haxi*M- Haziy*x)/eperp', ... 'Eazi','(-Haxix+Hrady)/eperp', ... 'Eaxi','(Hazi-Hrad*M+Hazix*x)/epara', ... 'ElecEn','log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-04)', ... 'Emag','log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-04)'}; % Descriptions clear descr descr.expr= {'Eaxi','axiall component of electric field strength','MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)','ElecEn','electric field energy density','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','Emag','electric field magnitude'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495805e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00362800835940596,0.0482685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-02) Contour: log10(Haxi*Haxi+1e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+1e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-04)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-04) Contour: log10(Haxi*Haxi+1e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-04)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-04) Contour: log10(Haxi*Haxi+1e-05) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-04)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-04) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, .t`.. 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',2.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Eaxi*Eaxi+1e-03)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Eaxi*Eaxi+1e-03) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-03) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00985575482644509,0.0544963446941628,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030372e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',15, ... 'phase',(0)*pi/180, ... 'title','lambda(15)=1.100861e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00933212937787436,0.0539727192455921,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00933212937787436,0.0539727192455921,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.205595e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00933212937787436,0.0539727192455921,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',12, ... 'phase',(0)*pi/180, ... 'title','lambda(12)=1.240562e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00933212937787436,0.0539727192455921,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00933212937787436,0.0539727192455921,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'deformsub',{'Hrad','Hazi'}, ... 'deformscale',1, ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi] Deformation: Hrad,Hazi', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00933212937787436,0.0539727192455921,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00933212937787436,0.0539727192455921,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00933212937787436,0.0539727192455921,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192519e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00933212937787436,0.0539727192455921,-1,1]); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[13],3,[50],5,[28],7,[14],14,[28],21,[30]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[13],3,[50],5,[24],7,[14],14,[28],21,[30]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[13],3,[50],5,[26],7,[14],14,[28],21,[30]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[15],3,[50],5,[26],7,[14],14,[28],21,[30]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[16],3,[50],5,[26],7,[14],14,[28],21,[30]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[18],3,[50],5,[26],7,[14],14,[28],21,[30]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[20],3,[50],5,[26],7,[14],14,[28],21,[30]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[20],3,[50],5,[26],7,[14],14,[28],21,[40]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[20],3,[50],5,[26],7,[14],14,[28],21,[34]}); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[20],3,[50],5,[26],7,[14],14,[28],21,[34]}); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'(-epara2*Haziy*M*test(Haxi)+eperp2*Hazix*test(Hazi)+eperp2*Hazi*test(Hazix)-eperp2*Hrad*M*test(Hazix)-epara2*Haxi*M*test(Haziy)-eperp2*Hazix*M*test(Hrad))/(epara2*eperp2)+(epara2*Haxi*M^2*test(Haxi)+eperp2*Hazi*test(Hazi)-eperp2*Hrad*M*test(Hazi)-eperp2*Hazi*M*test(Hrad)+eperp2*Hrad*M^2*test(Hrad))/(epara2*eperp2*x)+(x*(epara2*(Haxix-Hrady)*test(Haxix)+eperp2*Hazix*test(Hazix)+epara2*Haziy*test(Haziy)-epara2*Haxix*test(Hrady)+epara2*Hrady*test(Hrady)))/(epara2*eperp2)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara3*Haziy*M*test(Haxi)+eperp3*Hazix*test(Hazi)+eperp3*Hazi*test(Hazix)-eperp3*Hrad*M*test(Hazix)-epara3*Haxi*M*test(Haziy)-eperp3*Hazix*M*test(Hrad))/(epara3*eperp3)+(epara3*Haxi*M^2*test(Haxi)+eperp3*Hazi*test(Hazi)-eperp3*Hrad*M*test(Hazi)-eperp3*Hazi*M*test(Hrad)+eperp3*Hrad*M^2*test(Hrad))/(epara3*eperp3*x)+(x*(epara3*(Haxix-Hrady)*test(Haxix)+eperp3*Hazix*test(Hazix)+epara3*Haziy*test(Haziy)-epara3*Haxix*test(Hrady)+epara3*Hrady*test(Hrady)))/(epara3*eperp3)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara4*Haziy*M*test(Haxi)+eperp4*Hazix*test(Hazi)+eperp4*Hazi*test(Hazix)-eperp4*Hrad*M*test(Hazix)-epara4*Haxi*M*test(Haziy)-eperp4*Hazix*M*test(Hrad))/(epara4*eperp4)+(epara4*Haxi*M^2*test(Haxi)+eperp4*Hazi*test(Hazi)-eperp4*Hrad*M*test(Hazi)-eperp4*Hazi*M*test(Hrad)+eperp4*Hrad*M^2*test(Hrad))/(epara4*eperp4*x)+(x*(epara4*(Haxix-Hrady)*test(Haxix)+eperp4*Hazix*test(Hazix)+epara4*Haziy*test(Haziy)-epara4*Haxix*test(Hrady)+epara4*Hrady*test(Hrady)))/(epara4*eperp4)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'},{'(-epara5*Haziy*M*test(Haxi)+eperp5*Hazix*test(Hazi)+eperp5*Hazi*test(Hazix)-eperp5*Hrad*M*test(Hazix)-epara5*Haxi*M*test(Haziy)-eperp5*Hazix*M*test(Hrad))/(epara5*eperp5)+(epara5*Haxi*M^2*test(Haxi)+eperp5*Hazi*test(Hazi)-eperp5*Hrad*M*test(Hazi)-eperp5*Hazi*M*test(Hrad)+eperp5*Hrad*M^2*test(Hrad))/(epara5*eperp5*x)+(x*(epara5*(Haxix-Hrady)*test(Haxix)+eperp5*Hazix*test(Hazix)+epara5*Haziy*test(Haziy)-epara5*Haxix*test(Hrady)+epara5*Hrady*test(Hrady)))/(epara5*eperp5)'; ... 'alpha*(Hrad*test(Haxiy)-Hazi*M*test(Haxiy)-Haxiy*M*test(Hazi)-Hradx*M*test(Hazi)+Haxiy*test(Hrad)+Hradx*test(Hrad)+(-Hrad*M*test(Hazi)+Hazi*M^2*test(Hazi)+Hrad*test(Hrad)-Hazi*M*test(Hrad))/x+Hrad*test(Hradx)-Hazi*M*test(Hradx)+x*(Haxiy*test(Haxiy)+Hradx*test(Haxiy)+Haxiy*test(Hradx)+Hradx*test(Hradx)))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'}}; equ.name = {'dielectric_1','dielectric_0:vacuum','dielectric_2','dielectric_3', ... 'dielectric_4','dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1.00'}, ... 'epara',{'epara1','1.00'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','(Haxi*M- Haziy*x)/eperp', ... 'Eazi','(-Haxix+Hrady)/eperp', ... 'Eaxi','(Hazi-Hrad*M+Hazix*x)/epara', ... 'ElecEn','log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-04)', ... 'Emag','log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-04)'}; % Descriptions clear descr descr.expr= {'Eaxi','axiall component of electric field strength','MagEn','magnetic field energy density','DivH','divergence of magnetic field (should be zero)','ElecEn','electric field energy density','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','Emag','electric field magnitude'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'eperp2','relative permittivity of dielectric_2 perpendicular to cylindrical axis','c','speed of light (exact!)','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','eperp_293K_sapph','nominal room temperature values for same','epara1','relative permittivity of dielectric_1 parallel to cylindrical axis','eperp3','etc.','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc.','eperp1','relative permittivity of dielectric_1 perpendicular to cylindrical axis','delta_eperp1','small postivie finite number (to avoid close-to-zero values)','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495792e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00362800835940596,0.0482685982271237,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Haxi*Haxi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Haxi*Haxi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00575095251905018,0.0508788950590848,-0.00921223383123901,0.0538528236989567,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+3e-06)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Hazi*Hazi+3e-06) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-1.37503775071269E-4,0.045139673983454,-3.97834199044468E-4,0.05006965418058,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-05)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Hazi*Hazi+1e-05) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-1.37503775071269E-4,0.045139673983454,-7.72592776120882E-4,0.0504444127576565,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Hazi*Hazi) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-1.37503775071269E-4,0.045139673983454,-7.72592776120882E-4,0.0504444127576565,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-7)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Hazi*Hazi+1e-7) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-1.37503775071269E-4,0.045139673983454,-6.46442516185475E-4,0.050318262497721,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',10, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-1.37503775071269E-4,0.045139673983454,-0.00102867780378978,0.0507004977853253,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-1.37503775071269E-4,0.045139673983454,-0.00102867780378978,0.0507004977853253,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-1.37503775071269E-4,0.045139673983454,-0.00102867780378978,0.0507004977853253,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-1.37503775071269E-4,0.045139673983454,-0.00102867780378978,0.0507004977853253,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-02) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00732552473044753,0.0523276949388303,-3.97834199044468E-4,0.05006965418058,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.00', ... 'epara2','1.00', ... 'eperp3','1.00', ... 'epara3','1.00', ... 'eperp4','1.00', ... 'epara4','1.00', ... 'eperp5','1.00', ... 'epara5','1.00', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_e','0*1e-3', ... 'e1','9.8*(1+delta_e)', ... 'e2','1.0', ... 'e3','1.0', ... 'e4','1.0', ... 'e5','1.0', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.0', ... 'epara2','1.0', ... 'eperp3','1.0', ... 'epara3','1.0', ... 'eperp4','1.0', ... 'epara4','1.0', ... 'eperp5','1.0', ... 'epara5','1.0', ... 'e_293K_alumina','9.8', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_e','0*1e-3', ... 'e1','9.8*(1+delta_e)', ... 'e2','1.0', ... 'e3','1.0', ... 'e4','1.0', ... 'e5','1.0', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.0', ... 'epara2','1.0', ... 'eperp3','1.0', ... 'epara3','1.0', ... 'eperp4','1.0', ... 'epara4','1.0', ... 'eperp5','1.0', ... 'epara5','1.0', ... 'e_293K_alumina','9.8', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_e','0*1e-3', ... 'e1','9.8*(1+delta_e)', ... 'e2','1.0', ... 'e3','1.0', ... 'e4','1.0', ... 'e5','1.0', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.0', ... 'epara2','1.0', ... 'eperp3','1.0', ... 'epara3','1.0', ... 'eperp4','1.0', ... 'epara4','1.0', ... 'eperp5','1.0', ... 'epara5','1.0', ... 'e_293K_alumina','9.8', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_e','0*1e-3', ... 'e1','9.8*(1+delta_e)', ... 'e2','1.0', ... 'e3','1.0', ... 'e4','1.0', ... 'e5','1.0', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.0', ... 'epara2','1.0', ... 'eperp3','1.0', ... 'epara3','1.0', ... 'eperp4','1.0', ... 'epara4','1.0', ... 'eperp5','1.0', ... 'epara5','1.0', ... 'e_293K_alumina','9.8', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_e','0*1e-3', ... 'e1','9.8*(1+delta_e)', ... 'e2','1.0', ... 'e3','1.0', ... 'e4','1.0', ... 'e5','1.0', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.0', ... 'epara2','1.0', ... 'eperp3','1.0', ... 'epara3','1.0', ... 'eperp4','1.0', ... 'epara4','1.0', ... 'eperp5','1.0', ... 'epara5','1.0', ... 'e_293K_alumina','9.8', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_e','0*1e-3', ... 'e1','9.8*(1+delta_e)', ... 'e2','1.0', ... 'e3','1.0', ... 'e4','1.0', ... 'e5','1.0', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.0', ... 'epara2','1.0', ... 'eperp3','1.0', ... 'epara3','1.0', ... 'eperp4','1.0', ... 'epara4','1.0', ... 'eperp5','1.0', ... 'epara5','1.0', ... 'e_293K_alumina','9.8', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_e','0*1e-3', ... 'e1','9.8*(1+delta_e)', ... 'e2','1.0', ... 'e3','1.0', ... 'e4','1.0', ... 'e5','1.0', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.0', ... 'epara2','1.0', ... 'eperp3','1.0', ... 'epara3','1.0', ... 'eperp4','1.0', ... 'epara4','1.0', ... 'eperp5','1.0', ... 'epara5','1.0', ... 'e_293K_alumina','9.8', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_e','0*1e-3', ... 'e1','9.8*(1+delta_e)', ... 'e2','1.0', ... 'e3','1.0', ... 'e4','1.0', ... 'e5','1.0', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.0', ... 'epara2','1.0', ... 'eperp3','1.0', ... 'epara3','1.0', ... 'eperp4','1.0', ... 'epara4','1.0', ... 'eperp5','1.0', ... 'epara5','1.0', ... 'e_293K_alumina','9.8', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'-Hrad';'-Hazi';'-Haxi'}}; bnd.name = {'tangential_H',''}; bnd.ind = [1,1,1,2,1,2,1,2,1,2,2,2,2,1,2,1,2,2,2,2,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2; ... 3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp2*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara2*M^2*test(Haxi)*Haxi)/x+eperp2*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara2*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp2*test(Hazix)*Hazix+epara2*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara2*eperp2)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp3*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara3*M^2*test(Haxi)*Haxi)/x+eperp3*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara3*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp3*test(Hazix)*Hazix+epara3*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara3*eperp3)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp4*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara4*M^2*test(Haxi)*Haxi)/x+eperp4*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara4*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp4*test(Hazix)*Hazix+epara4*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara4*eperp4)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp5*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara5*M^2*test(Haxi)*Haxi)/x+eperp5*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara5*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp5*test(Hazix)*Hazix+epara5*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara5*eperp5)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e1'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e2'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e3'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e4'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e5'; ... 'alpha*((test(Ht`rad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0'; ... '0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.name = {'uniaxial_dielectric_1','dielectric_0:vacuum','uniaxial_dielectric_2', ... 'uniaxial_dielectric_3','uniaxial_dielectric_4','uniaxial_dielectric_5', ... 'isotropic_dielectric_1','isotropic_dielectric_2','isotropic_dielectric_3', ... 'isotropic_dielectric_4','isotropic_dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1'}, ... 'epara',{'epara1','1'}}; fem.equ = equ; % Global expressions fem.expr = {'HaziStr','log10(Hazi*Hazi+1e-6)', ... 'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','(Haxi*M- Haziy*x)/eperp', ... 'Eazi','(-Haxix+Hrady)/eperp', ... 'Eaxi','(Hazi-Hrad*M+Hazix*x)/epara', ... 'ElecEn','log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-4)', ... 'ElecStr','log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)'}; % Descriptions clear descr descr.expr= {'Eaxi','axial component of electric field strength','MagEn','logarithmic magnetic field energy density','DivH','divergence of magnetic field (should be zero!)','ElecEn','logarithmic electric energy density','HaziStr','logarithmic magnitude of azimuthal magnetic field strength','Eazi','azimuthal component of electric field strength','ElecStr','logarithmic magnitude of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'e_293K_alumina','relative permittivity of alumina at room temperature','e2','ditto for isotropic_dielectric_2','eperp2','relative permittivity of uniaxial_dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','c','speed of light (exact!)','delta_e','fractional increment (for determining filling factors)','e3','etc. ...','epara1','relative permittivity of uniaxial_dielectric_1 parallel to cylindrical axis','eperp3','etc.','delta_epara1','fractional increment (for determining filling factors)','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc. ...','e1','relative permittivity of isotropic_dielectric_1','eperp1','relative permittivity of uniaxial_dielectric_1 perpendicular to cylindrical axis','delta_eperp1','fractional increment (for determining filling factors)','eperp_4K_sapph_NPL','NPL values: fitted to resonance frequencies of NPL Cs HEMEX resonator','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'ElecStr','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'HaziStr','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495792e10 Surface: ElecStr Contour: HaziStr Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00238319682096284,0.0472968951434518,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecStr','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'HaziStr','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: ElecStr Contour: HaziStr Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00213568491890328,0.0470493832413922,-0.0025429524178502,0.0523359536821839,-1,1]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'Hazi';'-Haxi*nx+Hrad*ny';'0'},{'0'; ... '0';'0'}}; bnd.name = {'tangential_H','normal_H','null'}; bnd.ind = [1,1,1,3,1,3,1,3,1,3,3,3,3,1,3,1,3,3,3,3,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2; ... 3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp2*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara2*M^2*test(Haxi)*Haxi)/x+eperp2*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara2*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp2*test(Hazix)*Hazix+epara2*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara2*eperp2)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp3*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara3*M^2*test(Haxi)*Haxi)/x+eperp3*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara3*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp3*test(Hazix)*Hazix+epara3*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara3*eperp3)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp4*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara4*M^2*test(Haxi)*Haxi)/x+eperp4*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara4*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp4*test(Hazix)*Hazix+epara4*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara4*eperp4)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp5*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara5*M^2*test(Haxi)*Haxi)/x+eperp5*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara5*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp5*test(Hazix)*Hazix+epara5*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara5*eperp5)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e1'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e2'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e3'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e4'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e5'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0'; ... '0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.name = {'uniaxial_dielectric_1','dielectric_0:vacuum','uniaxial_dielectric_2', ... 'uniaxial_dielectric_3','uniaxial_dielectric_4','uniaxial_dielectric_5', ... 'isotropic_dielectric_1','isotropic_dielectric_2','isotropic_dielectric_3', ... 'isotropic_dielectric_4','isotropic_dielectric_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1'}, ... 'epara',{'epara1','1'}}; fem.equ = equ; % Global expressions fem.expr = {'HaziStr','log10(Hazi*Hazi+1e-6)', ... 'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','(Haxi*M- Haziy*x)/eperp', ... 'Eazi','(-Haxix+Hrady)/eperp', ... 'Eaxi','(Hazi-Hrad*M+Hazix*x)/epara', ... 'ElecEn','log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-4)', ... 'ElecStr','log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)'}; % Descriptions clear descr descr.expr= {'Eaxi','axial component of electric field strength','MagEn','logarithmic magnetic field energy density','DivH','divergence of magnetic field (should be zero!)','HaziStr','logarithmic magnitude of azimuthal magnetic field strength','ElecEn','logarithmic electric energy density','Eazi','azimuthal component of electric field strength','ElecStr','logarithmic magnitude of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Daxi','axial component of electric displacement','Erad','radial component of electric field strength'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'e_293K_alumina','relative permittivity of alumina at room temperature','e2','ditto for isotropic_dielectric_2','eperp2','relative permittivity of uniaxial_dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','c','speed of light (exact!)','delta_e','fractional increment (for determining filling factors)','e3','etc. ...','epara1','relative permittivity of uniaxial_dielectric_1 parallel to cylindrical axis','eperp3','etc.','delta_epara1','fractional increment (for determining filling factors)','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc. ...','eperp1','relative permittivity of uniaxial_dielectric_1 perpendicular to cylindrical axis','e1','relative permittivity of isotropic_dielectric_1','delta_eperp1','fractional increment (for determining filling factors)','alpha','penalty coefficient on Div H','eperp_4K_sapph_NPL','NPL values: fitted to resonance frequencies of NPL Cs HEMEX resonator'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'ElecStr','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'HaziStr','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495792e10 Surface: ElecStr Contour: HaziStr Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00937291637677534,0.0542866146992643,-0.00295454421360046,0.0527475454779342,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'ElecStr','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'HaziStr','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: ElecStr Contour: HaziStr Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00213568491890328,0.0470493832413922,-0.00335492266478335,0.0531479239291171,-1,1]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'HaziStr','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2) Contour: HaziStr Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0095134451429476,0.0544271434654365,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hazi','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hazi, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00213568491890328,0.0470493832413922,-0.00320046955440193,0.0529934708187357,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00213568491890328,0.0470493832413922,-0.00320046955440193,0.0529934708187357,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00213568491890328,0.0470493832413922,-0.00320046955440193,0.0529934708187357,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00213568491890328,0.0470493832413922,-0.00320046955440193,0.0529934708187357,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00213568491890328,0.0470493832413922,-0.00320046955440193,0.0529934708187357,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'Hazi';'-Haxi*nx+Hrad*ny';'0'},{'0'; ... '0';'0'}}; bnd.name = {'tangential_H','normal_H','null'}; bnd.ind = [1,1,1,3,1,3,1,3,1,3,3,3,3,1,3,1,3,3,3,3,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2; ... 3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp2*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara2*M^2*test(Haxi)*Haxi)/x+eperp2*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara2*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp2*test(Hazix)*Hazix+epara2*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara2*eperp2)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp3*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara3*M^2*test(Haxi)*Haxi)/x+eperp3*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara3*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp3*test(Hazix)*Hazix+epara3*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara3*eperp3)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp4*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara4*M^2*test(Haxi)*Haxi)/x+eperp4*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara4*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp4*test(Hazix)*Hazix+epara4*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara4*eperp4)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp5*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara5*M^2*test(Haxi)*Haxi)/x+eperp5*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara5*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp5*test(Hazix)*Hazix+epara5*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara5*eperp5)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e1'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e2'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e3'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e4'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e5'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0'; ... '0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.name = {'uniax_diel_1','dielectric_0:vacuum','uniax_diel_2','uniax_diel_3', ... 'uniax_diel_4','uniax_diel_5','isotrop_diel_1','isotrop_diel_2','isotrop_diel_3', ... 'isotrop_diel_4','isotrop_diel_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1'}, ... 'epara',{'epara1','1'}}; fem.equ = equ; % Global expressions fem.expr = {'HaziStr','log10(Hazi*Hazi+1e-6)', ... 'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEn','log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-6)', ... 'Drad','Haxi*M- Haziy*x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','Hazi-Hrad*M+Hazix*x', ... 'Erad','(Haxi*M- Haziy*x)/eperp', ... 'Eazi','(-Haxix+Hrady)/eperp', ... 'Eaxi','(Hazi-Hrad*M+Hazix*x)/epara', ... 'ElecEn','log10(Erad*Drad+Eazi*Dazi+Eaxi*Daxi+1e-4)', ... 'ElecStr','log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)'}; % Descriptions clear descr descr.expr= {'Eaxi','axial component of electric field strength','MagEn','logarithmic magnetic field energy density','DivH','divergence of magnetic field (should be zero!)','ElecEn','logarithmic electric energy density','HaziStr','logarithmic magnitude of azimuthal magnetic field strength','Eazi','azimuthal component of electric field strength','ElecStr','logarithmic magnitude of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'e_293K_alumina','relative permittivity of alumina at room temperature','e2','ditto for isotropic_dielectric_2','eperp2','relative permittivity of uniaxial_dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','c','speed of light (exact!)','delta_e','fractional increment (for determining filling factors)','e3','etc. ...','epara1','relative permittivity of uniaxial_dielectric_1 parallel to cylindrical axis','eperp3','etc.','delta_epara1','fractional increment (for determining filling factors)','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc. ...','e1','relative permittivity of isotropic_dielectric_1','eperp1','relative permittivity of uniaxial_dielectric_1 perpendicular to cylindrical axis','delta_eperp1','fractional increment (for determining filling factors)','eperp_4K_sapph_NPL','NPL values: fitted to resonance frequencies of NPL Cs HEMEX resonator','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495792e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00213568491890328,0.0470493832413922,-0.00320046955440193,0.0529934708187357,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Erad*Erad+Eazi*Eazi+Eaxi*Eaxi+1e-2) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00239533257084357,0.0473090308933325,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Hazi*Hazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-2) Contour: log10(Hazi*Hazi+1e-6) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00291640028652702,0.0478300986090159,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-6)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-2) Contour: log10(Eazi*Eazi+1e-6) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00291640028652702,0.0478300986090159,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-4)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-2) Contour: log10(Eazi*Eazi+1e-4) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00329699902824359,0.0482106973507325,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-2)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-2) Contour: log10(Eazi*Eazi+1e-2) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00329699902824359,0.0482106973507325,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-3)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-2) Contour: log10(Eazi*Eazi+1e-3) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00329699902824359,0.0482106973507325,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-3)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-3) Contour: log10(Eazi*Eazi+1e-3) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00329699902824359,0.0482106973507325,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-3)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-4) Contour: log10(Eazi*Eazi+1e-3) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00329699902824359,0.0482106973507325,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-4)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-4) Contour: log10(Eazi*Eazi+1e-4) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00329699902824359,0.0482106973507325,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-3)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-4) Contour: log10(Eazi*Eazi+1e-3) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00329699902824359,0.0482106973507325,-0.00307750688400119,0.0528705081483349,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-3)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-5) Contour: log10(Eazi*Eazi+1e-3) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00355073152272131,0.0484644298452102,-0.00307750688400119,0.0528705081483349,-1,1]); % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[20],3,[50],5,[26],7,[14],14,[28],21,[34]}); % Plot solution postplot(fem, ... 'tridata',{'log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-3)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(Hrad*Hrad+Hazi*Hazi+Haxi*Haxi+1e-5) Contour: log10(Eazi*Eazi+1e-3) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00991393281702475,0.0548276311395137,-0.00248965006321669,0.0522826513275504,-1,1]); % COMSOL Multiphyt`sics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'Hazi';'-Haxi*nx+Hrad*ny';'0'},{'0'; ... '0';'0'}}; bnd.name = {'tangential_H','normal_H','null'}; bnd.ind = [1,1,1,3,1,3,1,3,1,3,3,3,3,1,3,1,3,3,3,3,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2; ... 3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp2*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara2*M^2*test(Haxi)*Haxi)/x+eperp2*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara2*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp2*test(Hazix)*Hazix+epara2*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara2*eperp2)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp3*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara3*M^2*test(Haxi)*Haxi)/x+eperp3*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara3*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp3*test(Hazix)*Hazix+epara3*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara3*eperp3)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp4*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara4*M^2*test(Haxi)*Haxi)/x+eperp4*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara4*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp4*test(Hazix)*Hazix+epara4*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara4*eperp4)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp5*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara5*M^2*test(Haxi)*Haxi)/x+eperp5*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara5*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp5*test(Hazix)*Hazix+epara5*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara5*eperp5)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e1'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e2'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e3'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e4'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e5'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0'; ... '0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.name = {'uniax_diel_1','dielectric_0:vacuum','uniax_diel_2','uniax_diel_3', ... 'uniax_diel_4','uniax_diel_5','isotrop_diel_1','isotrop_diel_2','isotrop_diel_3', ... 'isotrop_diel_4','isotrop_diel_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1'}, ... 'epara',{'epara1','1'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEnDens','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi', ... 'Drad','(Haxi*M-Haziy*x)/x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','(Hazi-Hrad*M+Hazix*x)/x', ... 'Erad','Drad/erel', ... 'Eazi','Dazi/erel', ... 'Eaxi','Daxi/erel', ... 'ElecMagSqrd','Erad*Erad+Eazi*Eazi+Eaxi*Eaxi', ... 'ElecEnDens','Erad*Drad+Eazi*Dazi+Eaxi*Daxi'}; % Descriptions clear descr descr.expr= {'Eaxi','axial component of electric field strength','DivH','divergence of magnetic field (should be zero!)','ElecEnDens','electric energy density','ElecMagSqrd','electric field strength magnitude squared','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','MagEnDens','magnetic energy density'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'e_293K_alumina','relative permittivity of alumina at room temperature','e2','ditto for isotropic_dielectric_2','eperp2','relative permittivity of uniaxial_dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','c','speed of light (exact!)','delta_e','fractional increment (for determining filling factors)','e3','etc. ...','epara1','relative permittivity of uniaxial_dielectric_1 parallel to cylindrical axis','eperp3','etc.','delta_epara1','fractional increment (for determining filling factors)','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc. ...','eperp1','relative permittivity of uniaxial_dielectric_1 perpendicular to cylindrical axis','e1','relative permittivity of isotropic_dielectric_1','delta_eperp1','fractional increment (for determining filling factors)','alpha','penalty coefficient on Div H','eperp_4K_sapph_NPL','NPL values: fitted to resonance frequencies of NPL Cs HEMEX resonator'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'Hazi';'-Haxi*nx+Hrad*ny';'0'},{'0'; ... '0';'0'}}; bnd.name = {'tangential_H','normal_H','null'}; bnd.ind = [1,1,1,3,1,3,1,3,1,3,3,3,3,1,3,1,3,3,3,3,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2; ... 3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp2*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara2*M^2*test(Haxi)*Haxi)/x+eperp2*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara2*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp2*test(Hazix)*Hazix+epara2*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara2*eperp2)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp3*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara3*M^2*test(Haxi)*Haxi)/x+eperp3*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara3*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp3*test(Hazix)*Hazix+epara3*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara3*eperp3)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp4*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara4*M^2*test(Haxi)*Haxi)/x+eperp4*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara4*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp4*test(Hazix)*Hazix+epara4*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara4*eperp4)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp5*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara5*M^2*test(Haxi)*Haxi)/x+eperp5*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara5*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp5*test(Hazix)*Hazix+epara5*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara5*eperp5)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e1'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e2'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e3'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e4'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e5'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0'; ... '0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.name = {'uniax_diel_1','dielectric_0:vacuum','uniax_diel_2','uniax_diel_3', ... 'uniax_diel_4','uniax_diel_5','isotrop_diel_1','isotrop_diel_2','isotrop_diel_3', ... 'isotrop_diel_4','isotrop_diel_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1'}, ... 'epara',{'epara1','1'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEnDens','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi', ... 'Drad','(Haxi*M-Haziy*x)/x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','(Hazi-Hrad*M+Hazix*x)/x', ... 'Erad','Drad/eperp', ... 'Eazi','Dazi/eperp', ... 'Eaxi','Daxi/epara', ... 'ElecMagSqrd','Erad*Erad+Eazi*Eazi+Eaxi*Eaxi', ... 'ElecEnDens','Erad*Drad+Eazi*Dazi+Eaxi*Daxi'}; % Descriptions clear descr descr.expr= {'Eaxi','axial component of electric field strength','DivH','divergence of magnetic field (should be zero!)','ElecEnDens','electric energy density','ElecMagSqrd','electric field strength magnitude squared','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','MagEnDens','magnetic energy density'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'e_293K_alumina','relative permittivity of alumina at room temperature','e2','ditto for isotropic_dielectric_2','eperp2','relative permittivity of uniaxial_dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','c','speed of light (exact!)','delta_e','fractional increment (for determining filling factors)','e3','etc. ...','epara1','relative permittivity of uniaxial_dielectric_1 parallel to cylindrical axis','eperp3','etc.','delta_epara1','fractional increment (for determining filling factors)','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc. ...','eperp1','relative permittivity of uniaxial_dielectric_1 perpendicular to cylindrical axis','e1','relative permittivity of isotropic_dielectric_1','delta_eperp1','fractional increment (for determining filling factors)','alpha','penalty coefficient on Div H','eperp_4K_sapph_NPL','NPL values: fitted to resonance frequencies of NPL Cs HEMEX resonator'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem,'geoms',[1],'eqvars','on','cplbndeq','on','cplbndsh','off'); % Solve problem fem.sol=femeig(fem, ... 'method','eliminate', ... 'nullfun','auto', ... 'blocksize',5000, ... 'complexfun','off', ... 'solfile','off', ... 'conjugate','off', ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'rowscale','on', ... 'neigs',16, ... 'shift',0, ... 'krylovdim',0, ... 'maxeigit',300, ... 'etol',0.0, ... 'linsolver','spooles', ... 'thresh',0.1, ... 'preorder','mmd', ... 'uscale','auto', ... 'mcase',0); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-3)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',1, ... 'phase',(0)*pi/180, ... 'title','lambda(1)=1.495792e10 Surface: log10(MagEnDens+1e-5) Contour: log10(Eazi*Eazi+1e-3) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0117097954362115,0.0566234937587005,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-3)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[0.0,0.0,0.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Contour: log10(Eazi*Eazi+1e-3) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00545765170832655,0.0503713500308155,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00545765170832655,0.0503713500308155,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','off', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Constants fem.const = {'c','299792458', ... 'fc','4*pi^2/c^2', ... 'alpha','1', ... 'M','14', ... 'delta_e','0*1e-3', ... 'e1','9.8*(1+delta_e)', ... 'e2','1.0', ... 'e3','1.0', ... 'e4','1.0', ... 'e5','1.0', ... 'delta_eperp1','0*1e-3', ... 'eperp1','9.2725*(1+delta_eperp1)', ... 'delta_epara1','0*1e-3', ... 'epara1','11.3486*(1+delta_epara1)', ... 'eperp2','1.0', ... 'epara2','1.0', ... 'eperp3','1.0', ... 'epara3','1.0', ... 'eperp4','1.0', ... 'epara4','1.0', ... 'eperp5','1.0', ... 'epara5','1.0', ... 'e_293K_alumina','9.8', ... 'eperp_4K_sapph_UWA','9.2725', ... 'epara_4K_sapph_UWA','11.3486', ... 'eperp_293K_sapph','9.407', ... 'epara_293K_sapph','11.62', ... 'eperp_4K_sapph_NPL','9.2848', ... 'epara_4K_sapph_NPL','11.3660'}; % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',11, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',9, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',9, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',10, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',8, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',6, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',7, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',7, ... 'arrowscale',1.4, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',15, ... 'arrowyspacing',8, ... 'arrowscale',1.4, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',1.4, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(MagEnDens+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',1.4, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(MagEnDens+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e-5)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',1.4, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e-5) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e-3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',1.4, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e-3) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Hrad','Haxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',1.4, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e+0) Arrow: [Hrad, Haxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',1.4, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',1.0, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e+1)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e+1) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e+2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e+2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',14, ... 'arrowyspacing',8, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',10, ... 'arrowyspacing',14, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',10, .t`.. 'arrowyspacing',15, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',10, ... 'arrowyspacing',16, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',10, ... 'arrowyspacing',14, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',12, ... 'arrowyspacing',14, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',8, ... 'arrowyspacing',14, ... 'arrowscale',0.9, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',8, ... 'arrowyspacing',14, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',9, ... 'arrowyspacing',14, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',10, ... 'arrowyspacing',14, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',10, ... 'arrowyspacing',14, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',10, ... 'arrowyspacing',14, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',7, ... 'arrowyspacing',14, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',5, ... 'arrowyspacing',14, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.2, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+4)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+4) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log10(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eazi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log10(ElecMagSqrd+1e+3) Arrow: [Erad, Eazi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eazi','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: Eazi Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00814343176044616,0.0530571300829351,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'contdata',{'log10(Eazi*Eazi+1e-3)','cont','internal'}, ... 'contlevels',8, ... 'contstyle',[1.0,1.0,1.0], ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+3) Contour: log10(Eazi*Eazi+1e-3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00545765170832655,0.0503713500308155,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',3, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',4, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',2, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',3, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',4, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',5, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+3)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+3) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00849566520990447,0.0534093635323934,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi*Eaxi+0*log(ElecMagSqrd+1e+2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: Eaxi*Eaxi+0*log(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00840760684753989,0.0533213051700288,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi*Eaxi+0*log(ElecMagSqrd+1e+2)','cont','internal'}, ... 'tridlim',[1.0554683946511696E-30 10.71939644473], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: Eaxi*Eaxi+0*log(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00787925667335243,0.0527929549958414,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi*Eaxi+0*log(ElecMagSqrd+1e+2)','cont','internal'}, ... 'tridlim',[1.0554683946511696E-30 100.71939644473], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: Eaxi*Eaxi+0*log(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00787925667335243,0.0527929549958414,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi*Eaxi+0*log(ElecMagSqrd+1e+2)','cont','internal'}, ... 'tridlim',[1.0554683946511696E-30 10000.71939644473], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: Eaxi*Eaxi+0*log(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00787925667335243,0.0527929549958414,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Eaxi*Eaxi+0*log(ElecMagSqrd+1e+2)','cont','internal'}, ... 'tridlim',[1.0554683946511696E-30 1000.71939644473], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: Eaxi*Eaxi+0*log(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00787925667335243,0.0527929549958414,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+2)','cont','internal'}, ... 'tridlim',[1.0554683946511696E-30 1000.71939644473], ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00787925667335243,0.0527929549958414,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00787925667335243,0.0527929549958414,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+2)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+2) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+1)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+1) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','gray(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'-log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: -log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',13, ... 'phase',(0)*pi/180, ... 'title','lambda(13)=1.205583e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030366e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','off'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030366e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030366e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','off', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030366e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00823149012281074,0.0531451884452997,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum','end', ... 'phase',(0)*pi/180, ... 'title','lambda(16)=1.030366e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0117097954362115,0.0566234937587005,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00840760684753989,0.0533213051700288,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.00840760684753989,0.0533213051700288,-0.00248965006321669,0.0522826513275504,-1,1]); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'Hazi';'-Haxi*nx+Hrad*ny';'0'},{'0'; ... '0';'0'}}; bnd.name = {'tangential_H','normal_H','null'}; bnd.ind = [1,1,1,3,1,3,1,3,1,3,3,3,3,1,3,1,3,3,3,3,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2; ... 3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp2*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara2*M^2*test(Haxi)*Haxi)/x+eperp2*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara2*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp2*test(Hazix)*Hazix+epara2*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara2*eperp2)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp3*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara3*M^2*test(Haxi)*Haxi)/x+eperp3*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara3*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp3*test(Hazix)*Hazix+epara3*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara3*eperp3)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp4*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara4*M^2*test(Haxi)*Haxi)/x+eperp4*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara4*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp4*test(Hazix)*Hazix+epara4*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara4*eperp4)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp5*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara5*M^2*test(Haxi)*Haxi)/x+eperp5*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara5*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp5*test(Hazix)*Hazix+epara5*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara5*eperp5)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e1'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e2'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e3'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e4'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e5'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0'; ... '0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.name = {'uniax_diel_1','dielectric_0:vacuum','uniax_diel_2','uniax_diel_3', ... 'uniax_diel_4','uniax_diel_5','isotrop_diel_1','isotrop_diel_2','isotrop_diel_3', ... 'isotrop_diel_4','isotrop_diel_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1'}, ... 'epara',{'epara1','1'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEnDens','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi', ... 'Drad','(Haxi*M-Haziy*x)/x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','(Hazi-Hrad*M+Hazix*x)/x', ... 'Erad','Drad/eperp', ... 'Eazi','Dazi/eperp', ... 'Eaxi','Daxi/epara', ... 'ElecMagSqrd','Erad*Erad+Eazi*Eazi+Eaxi*Eaxi', ... 'ElecEnDens','Erad*Drad+Eazi*Dazi+Eaxi*Daxi'}; % Descriptions clear descr descr.expr= {'Eaxi','axial component of electric field strength','DivH','divergence of magnetic field (should be zero!)','ElecEnDens','electric energy density','ElecMagSqrd','electric field strength magnitude squared','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','MagEnDens','magnetic energy density'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'e_293K_alumina','relative permittivity of alumina at room temperatture','e2','ditto for isotropic_dielectric_2','eperp2','relative permittivity of uniaxial_dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','c','speed of light (exact!)','delta_e','fractional increment (for determining filling factors)','e3','etc. ...','epara1','relative permittivity of uniaxial_dielectric_1 parallel to cylindrical axis','eperp3','etc.','delta_epara1','fractional increment (for determining filling factors)','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc. ...','e1','relative permittivity of isotropic_dielectric_1','eperp1','relative permittivity of uniaxial_dielectric_1 perpendicular to cylindrical axis','delta_eperp1','fractional increment (for determining filling factors)','eperp_4K_sapph_NPL','NPL values: fitted to resonance frequencies of NPL Cs HEMEX resonator','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'Hazi';'-Haxi*nx+Hrad*ny';'0'},{'0'; ... '0';'0'}}; bnd.name = {'tangential_H','normal_H','null'}; bnd.ind = [1,1,1,3,1,3,1,3,1,3,3,3,3,1,3,1,3,3,3,3,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2; ... 3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp2*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara2*M^2*test(Haxi)*Haxi)/x+eperp2*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara2*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp2*test(Hazix)*Hazix+epara2*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara2*eperp2)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp3*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara3*M^2*test(Haxi)*Haxi)/x+eperp3*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara3*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp3*test(Hazix)*Hazix+epara3*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara3*eperp3)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp4*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara4*M^2*test(Haxi)*Haxi)/x+eperp4*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara4*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp4*test(Hazix)*Hazix+epara4*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara4*eperp4)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp5*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara5*M^2*test(Haxi)*Haxi)/x+eperp5*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara5*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp5*test(Hazix)*Hazix+epara5*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara5*eperp5)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e1'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e2'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e3'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e4'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e5'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0'; ... '0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.name = {'uniax_diel_1','dielectric_0:vacuum','uniax_diel_2','uniax_diel_3', ... 'uniax_diel_4','uniax_diel_5','isotrop_diel_1','isotrop_diel_2','isotrop_diel_3', ... 'isotrop_diel_4','isotrop_diel_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1'}, ... 'epara',{'epara1','1'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEnDens','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi', ... 'Drad','(Haxi*M-Haziy*x)/x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','(Hazi-Hrad*M+Hazix*x)/x', ... 'Erad','Drad/eperp', ... 'Eazi','Dazi/eperp', ... 'Eaxi','Daxi/epara', ... 'ElecMagSqrd','Erad*Erad+Eazi*Eazi+Eaxi*Eaxi', ... 'ElecEnDens','Erad*Drad+Eazi*Dazi+Eaxi*Daxi'}; % Descriptions clear descr descr.expr= {'Eaxi','axial component of electric field strength','DivH','divergence of magnetic field (should be zero!)','ElecEnDens','electric energy density','ElecMagSqrd','electric field strength magnitude squared','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','MagEnDens','magnetic energy density'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'e_293K_alumina','relative permittivity of alumina at room temperature','e2','ditto for isotropic_dielectric_2','eperp2','relative permittivity of uniaxial_dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','c','speed of light (exact!)','delta_e','fractional increment (for determining filling factors)','e3','etc. ...','epara1','relative permittivity of uniaxial_dielectric_1 parallel to cylindrical axis','eperp3','etc.','delta_epara1','fractional increment (for determining filling factors)','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc. ...','eperp1','relative permittivity of uniaxial_dielectric_1 perpendicular to cylindrical axis','e1','relative permittivity of isotropic_dielectric_1','delta_eperp1','fractional increment (for determining filling factors)','alpha','penalty coefficient on Div H','eperp_4K_sapph_NPL','NPL values: fitted to resonance frequencies of NPL Cs HEMEX resonator'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0110631081567644,0.0559768064792534,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0110631081567644,0.0559768064792534,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0110631081567644,0.0559768064792534,-0.00484588660292805,0.0546388878672618,-1,1]); % Integrate I1=postint(fem,'MagEnDens', ... 'dl',[1,2,3,4,5,6,7,8,9], ... 'edim',2, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Integrate I2=postint(fem,'2*pi*x*MagEnDens', ... 'dl',[1,2,3,4,5,6,7,8,9], ... 'edim',2, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Integrate I3=postint(fem,'2*pi*x*MagEnDens', ... 'dl',[1,2,3,4,5,6,7,8,9], ... 'edim',2, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Integrate I4=postint(fem,'2*pi*x*(Hazi^2*nx^2)', ... 'dl',[], ... 'edim',1, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Integrate I5=postint(fem,'2*pi*x*(Hazi^2*nx^2)', ... 'dl',[], ... 'edim',1, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Integrate I6=postint(fem,'2*pi*x*(Hazi^2*nx^2)', ... 'dl',[2,7,9,14,16,21,22,23,24], ... 'edim',1, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Integrate I7=postint(fem,'2*pi*x*(Hazi^2*nx^2)', ... 'dl',[2,7,9,14,16,21,22,23,24], ... 'edim',1, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Integrate I8=postint(fem,'2*pi*x*(Hazi^2*(nx^2+ny^2)+(Haxi*nx-Hrad*ny)^2)', ... 'dl',[2,7,9,14,16,21,22,23,24], ... 'edim',1, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Integrate I9=postint(fem,'2*pi*x*(Hazi^2*(nx^2+ny^2)+(Haxi*nx-Hrad*ny)^2)', ... 'dl',[2,7,9,14,16,21,22,23,24], ... 'edim',1, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'triedgestyle','none', ... 'trifacestyle','interp', ... 'tribar','on', ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'phase',(0)*pi/180, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'geom','on', ... 'geomnum',[1], ... 'sdl',{[1,2,3,4,5,6,7,8,9]}, ... 'axisvisible','on', ... 'axisequal','on', ... 'grid','off', ... 'axis',[-0.0110631081567644,0.0559768064792534,-0.00248965006321669,0.0522826513275504,-1,1]); % Integrate I10=postint(fem,'2*pi*x*MagEnDens', ... 'dl',[1,2,3,4,5,6,7,8,9], ... 'edim',2, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Integrate I11=postint(fem,'2*pi*x*(Hazi^2*(nx^2+ny^2)+(Haxi*nx-Hrad*ny)^2)', ... 'dl',[2,7,9,14,16,21,22,23,24], ... 'edim',1, ... 'intorder',4, ... 'geomnum',1, ... 'solnum',14, ... 'phase',(0)*pi/180); % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.mode.type = 'cartesian'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.sdim = {'x','y','z'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.shape = {'shlag(2,''Hrad'')','shlag(2,''Hazi'')','shlag(2,''Haxi'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear prop prop.elemdefault='Lag2'; prop.wave='off'; prop.frame='xy'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2','lm3','lm4','lm5','lm6'}; prop.weakconstr = weakconstr; appl.prop = prop; clear pnt pnt.weak = {{'0';'0';'0'}}; pnt.dweak = {{'0';'0';'0'}}; pnt.constr = {{'0';'0';'0'}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.weak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.dweak = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'}}; bnd.constr = {{'Hrad*nx+Haxi*ny';'0';'0'},{'Hazi';'-Haxi*nx+Hrad*ny';'0'},{'0'; ... '0';'0'}}; bnd.name = {'tangential_H','normal_H','null'}; bnd.ind = [1,1,1,3,1,3,1,3,1,3,3,3,3,1,3,1,3,3,3,3,1,1,1,1]; appl.bnd = bnd; clear equ equ.gporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.init = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.shape = {[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2;3],[1;2; ... 3],[1;2;3],[1;2;3],[1;2;3]}; equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp2*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara2*M^2*test(Haxi)*Haxi)/x+eperp2*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara2*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp2*test(Hazix)*Hazix+epara2*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara2*eperp2)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp3*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara3*M^2*test(Haxi)*Haxi)/x+eperp3*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara3*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp3*test(Hazix)*Hazix+epara3*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara3*eperp3)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp4*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara4*M^2*test(Haxi)*Haxi)/x+eperp4*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara4*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp4*test(Hazix)*Hazix+epara4*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara4*eperp4)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((eperp5*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara5*M^2*test(Haxi)*Haxi)/x+eperp5*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara5*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp5*test(Hazix)*Hazix+epara5*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara5*eperp5)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e1'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e2'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e3'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e4'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'},{'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e5'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'; ... '0'}}; equ.dweak = {{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'},{'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; ... '0';'0'}}; equ.usage = {1,1,1,1,1,1,1,1,1,1,1}; equ.constr = {{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0'; ... '0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0';'0'},{'0';'0'; ... '0'},{'0';'0';'0'}}; equ.cporder = {{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1;1},{1;1; ... 1},{1;1;1},{1;1;1},{1;1;1}}; equ.dinit = {{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0'; ... '0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0'; ... '0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'}, ... {'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0';'0'},{'0';'0';'0';'0';'0'; ... '0'}}; equ.name = {'uniax_diel_1','dielectric_0:vacuum','uniax_diel_2','uniax_diel_3', ... 'uniax_diel_4','uniax_diel_5','isotrop_diel_1','isotrop_diel_2','isotrop_diel_3', ... 'isotrop_diel_4','isotrop_diel_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.sdim = {'x','y'}; fem.frame = {'xy'}; % Simplify expressions fem.simplify = 'on'; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.var = {}; equ.expr = {'eperp',{'eperp1','1'}, ... 'epara',{'epara1','1'}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEnDens','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi', ... 'Drad','(Haxi*M-Haziy*x)/x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','(Hazi-Hrad*M+Hazix*x)/x', ... 'Erad','Drad/eperp', ... 'Eazi','Dazi/eperp', ... 'Eaxi','Daxi/epara', ... 'ElecMagSqrd','Erad*Erad+Eazi*Eazi+Eaxi*Eaxi', ... 'ElecEnDens','Erad*Drad+Eazi*Dazi+Eaxi*Daxi'}; % Descriptions clear descr descr.expr= {'Eaxi','axial component of electric field strength','DivH','divergence of magnetic field (should be zero!)','ElecEnDens','electric energy density','ElecMagSqrd','electric field strength magnitude squared','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','MagEnDens','magnetic energy density'}; fem.descr = descr; % Functions clear fcns fem.functions = {}; % Descriptions descr = fem.descr; descr.const= {'e_293K_alumina','relative permittivity of alumina at room temperature','e2','ditto for isotropic_dielectric_2','eperp2','relative permittivity of uniaxial_dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','c','speed of light (exact!)','delta_e','fractional increment (for determining filling factors)','e3','etc. ...','epara1','relative permittivity of uniaxial_dielectric_1 parallel to cylindrical axis','eperp3','etc.','delta_epara1','fractional increment (for determining filling factors)','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc. ...','e1','relative permittivity of isotropic_dielectric_1','eperp1','relative permittivity of uniaxial_dielectric_1 perpendicular to cylindrical axis','delta_eperp1','fractional increment (for determining filling factors)','eperp_4K_sapph_NPL','NPL values: fitted to resonance frequencies of NPL Cs HEMEX resonator','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Solution form fem.solform = 'weak'; % Multiphysics fem=multiphysics(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Create mapped quad mesh fem.mesh=meshmap(fem, ... 'edgegroups',{{[2],[8],[4],[1]},{},{},{},{},{},{},{},{}}, ... 'edgelem',{1,[10],3,[25],5,[13],7,[7],14,[14],21,[17]}); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.2 (COMSOL 3.2.0.224, $Date: 2005/10/24 07:30:19 $) % Some geometry objects are stored in a separate file. % The name of this file is given by the variable 'flbinaryfile'. flbinaryfile=''; % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'axis',[-0.0147898041622324,0.0597035024847213,-0.00248965006321669,0.0522826513275504,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',14, ... 'title','lambda(14)=1.192515e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'axis',[-0.0147898041622324,0.0597035024847213,-0.00248965006321669,0.0522826513275504,-1,1]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'FlPDEW'; appl.dim = {'Hrad','Hazi','Haxi','Hrad_t','Hazi_t','Haxi_t'}; appl.name = 'Axisymmetric_Dielectric_Resonator_Simulator'; appl.gporder = 4; appl.cporder = 2; appl.assignsuffix = '_Axisymmetric_Dielectric_Resonator_Simulator'; clear bnd bnd.constr = {'Hrad*nx+Haxi*ny',{'Hazi';'-Haxi*nx+Hrad*ny'},0}; bnd.name = {'tangential_H','normal_H','null'}; bnd.ind = [1,1,1,3,1,3,1,3,1,3,3,3,3,1,3,1,3,3,3,3,1,1,1,1]; appl.bnd = bnd; clear equ equ.weak = {{'((eperp1*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara1*M^2*test(Haxi)*Haxi)/x+eperp1*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara1*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp1*test(Hazix)*Hazix+epara1*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara1*eperp1)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}, ... {'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}, ... {'((eperp2*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara2*M^2*test(Haxi)*Haxi)/x+eperp2*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara2*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp2*test(Hazix)*Hazix+epara2*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara2*eperp2)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}, ... {'((eperp3*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara3*M^2*test(Haxi)*Haxi)/x+eperp3*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara3*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp3*test(Hazix)*Hazix+epara3*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara3*eperp3)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}, ... {'((eperp4*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara4*M^2*test(Haxi)*Haxi)/x+eperp4*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara4*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp4*test(Hazix)*Hazix+epara4*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara4*eperp4)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}, ... {'((eperp5*(test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hrad)*Hrad)+epara5*M^2*test(Haxi)*Haxi)/x+eperp5*(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-epara5*M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(eperp5*test(Hazix)*Hazix+epara5*((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/(epara5*eperp5)'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}, ... {'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e1'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}, ... {'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e2'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}, ... {'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e3'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}, ... {'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e4'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}, ... {'((test(Hazi)*Hazi-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*(test(Hrad)*Hrad+test(Haxi)*Haxi))/x+(test(Hazix)*(Hazi-M*Hrad)+Hazix*(test(Hazi)-M*test(Hrad)))-M*(test(Haxi)*Haziy+Haxi*test(Haziy))+x*(test(Hazix)*Hazix+((test(Haxix)-test(Hrady))*(Haxix-Hrady)+Haziy*test(Haziy))))/e5'; ... 'alpha*((test(Hrad)*Hrad-M*(test(Hazi)*Hrad+Hazi*test(Hrad))+M^2*test(Hazi)*Hazi)/x+(test(Haxiy)+test(Hradx))*(Hrad-M*Hazi)+(test(Hrad)-M*test(Hazi))*(Hradx+Haxiy)+x*(test(Hradx)+test(Haxiy))*(Hradx+Haxiy))'}}; equ.dweak = 'fc*x*(Haxitt*test(Haxi)+Hazitt*test(Hazi)+Hradtt*test(Hrad))'; equ.name = {'uniax_diel_1','dielectric_0:vacuum','uniax_diel_2','uniax_diel_3', ... 'uniax_diel_4','uniax_diel_5','isotrop_diel_1','isotrop_diel_2','isotrop_diel_3', ... 'isotrop_diel_4','isotrop_diel_5'}; equ.ind = [1,1,1,2,1,2,2,2,2]; appl.equ = equ; fem.appl{1} = appl; fem.border = 1; fem.units = 'SI'; % Subdomain expressions clear equ equ.ind = [1,1,1,2,1,2,2,2,2]; equ.dim = {'Hrad','Hazi','Haxi'}; equ.expr = {'eperp',{'eperp1',1}, ... 'epara',{'epara1',1}}; fem.equ = equ; % Global expressions fem.expr = {'DivH','(Hrad-Hazi*M+(Haxiy+Hradx)*x)/x', ... 'MagEnDens','Hrad*Hrad+Hazi*Hazi+Haxi*Haxi', ... 'Drad','(Haxi*M-Haziy*x)/x', ... 'Dazi','-Haxix+Hrady', ... 'Daxi','(Hazi-Hrad*M+Hazix*x)/x', ... 'Erad','Drad/eperp', ... 'Eazi','Dazi/eperp', ... 'Eaxi','Daxi/epara', ... 'ElecMagSqrd','Erad*Erad+Eazi*Eazi+Eaxi*Eaxi', ... 'ElecEnDens','Erad*Drad+Eazi*Dazi+Eaxi*Daxi'}; % Descriptions clear descr descr.expr= {'Eaxi','axial component of electric field strength','DivH','divergence of magnetic field (should be zero!)','ElecEnDens','electric energy density','ElecMagSqrd','electric field strength magnitude squared','Eazi','azimuthal component of electric field strength','Drad','radial component of electric displacement','Dazi','azimuthal component of electric displacement','Erad','radial component of electric field strength','Daxi','axial component of electric displacement','MagEnDens','magnetic energy density'}; fem.descr = descr; % Descriptions descr = fem.descr; descr.const= {'e_293K_alumina','relative permittivity of alumina at room temperature','e2','ditto for isotropic_dielectric_2','eperp2','relative permittivity of uniaxial_dielectric_2 perpendicular to cylindrical axis','eperp_293K_sapph','nominal room temperature values for same','eperp_4K_sapph_UWA','UWA values for cryogenic HEMEX sapphire','c','speed of light (exact!)','delta_e','fractional increment (for determining filling factors)','e3','etc. ...','epara1','relative permittivity of uniaxial_dielectric_1 parallel to cylindrical axis','eperp3','etc.','delta_epara1','fractional increment (for determining filling factors)','epara2','ditto but parallel to cylindrical axis','M','azimuthal mode order','fc','constant used internally --do not modify','epara3','etc. ...','e1','relative permittivity of isotropic_dielectric_1','eperp1','relative permittivity of uniaxial_dielectric_1 perpendicular to cylindrical axis','delta_eperp1','fractional increment (for determining filling factors)','eperp_4K_sapph_NPL','NPL values: fitted to resonance frequencies of NPL Cs HEMEX resonator','alpha','penalty coefficient on Div H'}; fem.descr = descr; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femeig(fem, ... 'symmetric','on', ... 'solcomp',{'Hazi','Haxi','Hrad'}, ... 'outcomp',{'Hazi','Haxi','Hrad'}, ... 'neigs',3, ... 'linsolver','spooles'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'log(ElecMagSqrd+1e+0)','cont','internal'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Erad','Eaxi'}, ... 'arrowxspacing',6, ... 'arrowyspacing',14, ... 'arrowscale',1.3, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,1.0,1.0], ... 'solnum',1, ... 'title','lambda(1)=1.192565e10 Surface: log(ElecMagSqrd+1e+0) Arrow: [Erad, Eaxi]', ... 'refine',3, ... 'axis',[-0.0125701888828511,0.05748388720534,-0.00248965006321669,0.0522826513275504,-1,1]); tfemsq~wt COMSOL 3.2twt $Name: $t$Date: 2005/10/24 07:30:19 $xxur[[Ljava.lang.String;2M 2Wxpuq~ +q~q~q~ q~!q~"q~#q~$q~%q~&q~'q~(q~)q~*q~+q~,q~-q~.q~/q~0q~1q~2q~3q~4q~5q~6q~7q~8q~9q~:q~;q~q~?q~@q~Aq~Bq~Cq~Dq~Eq~Fq~Gq~Huq~ +q~Sq~Sq~Sq~Sq~Tq~Sq~Sq~Tq~Sq~Sq~Sq~Sq~Sq~Sq~Tq~Sq~Sq~Sq~Tq~Sq~Tq~Sq~Sq~Sq~Tq~Sq~Sq~Tq~Tq~Sq~Sq~Tq~Sq~Sq~Sq~Sq~Sq~Sq~Sq~Sq~Sq~Uq~S