[讨论]有用MATLAB做FDTD的进

这个程序不是很清楚，望各位大虾或同道中人一起研究。我的QQ：67715710.请注明FDTD. pe+h8  
%*********************************************************************** Px \cT  
%     3-D FDTD code with UPML absorbing boundary conditions L*A-&9.p3  
%*********************************************************************** emnT;kJ>  
% pWJEFm  
%     Program author: Keely J. Willis, Graduate Student 6b'.WB]-  
%                     UW Computational Electromagnetics Laboratory S**eI<QFSk  
%                           Director: Susan C. Hagness wB \`3u4  
%                     Department of Electrical and Computer Engineering  <EN9s  
%                     University of Wisconsin-Madison \y=oZk4  
%                     1415 Engineering Drive vI5lp5( -3  
%                     Madison, WI 53706-1691 [x>Ju&))$  
%                     [url=mailto:kjwillis@wisc.edu]kjwillis@wisc.edu[/url] !%('8-x%  
% )S2yU<6oOt  
%     Copyright 2005 hp9U   
% 4m1r@ $  
%     This MATLAB M-file implements the finite-difference time-domain DHw)]WB M  
%     solution of Maxwell's curl equations over a three-dimensional W [K.|8ho  
%     Cartesian space lattice comprised of uniform cubic grid cells. 1nskf*Z  
%     mJk\$/Kh  
%     The dimensions of the computational domain are 8.2 cm sTlel&  
%     (x-direction), 3.4 cm (y-direction), and 3.2 cm (z-direction).  zp1ym}9M  
%     The grid is terminated with UPML absorbing boundary conditions. \'*M }G  
% ` K{k0_{  
%     An electric current source comprised of two collinear Jz components ]FTi2B{}H  
%     (realizing a Hertzian dipole) excites a radially propagating wave.  z^Ikb(KC  
%     The current source is located in the center of the grid.  The <]LljTm`i  
%     source waveform is a differentiated Gaussian pulse given by [{BY$"b#:  
%          J(t)=J0*(t-t0)*exp(-(t-t0)^2/tau^2), c:9n8skE7  
%     where tau=50 ps.  The FWHM spectral bandwidth of this zero-dc- 5Q"w{ n  
%     content pulse is approximately 7 GHz. The grid resolution Q zaD\^OF  
%     (dx = 2 mm) was chosen to provide at least 10 samples per RLnL9)`W  
%     wavelength up through 15 GHz. Q^rR}Ws  
% uu,F5<y[  
%     To execute this M-file, type "fdtd3D_UPML" at the MATLAB prompt.  Op?"G  
% 'OziP  
%     This code has been tested in the following Matlab environments: N6}/TbfAR  
%     Matlab version 6.1.0.450 Release 12.1 (May 18, 2001) oYStf5  
%     Matlab version 6.5.1.199709 Release 13 Service Pack 1 (August 4, 2003) H%>4z3n   
%     Matlab version 7.0.0.19920 R14 (May 6, 2004) y@!o&,,mq  
%     Matlab version 7.0.1.24704 R14 Service Pack 1 (September 13, 2004)  xV5UaD<  
%     Matlab version 7.0.4.365 R14 Service Pack 2 (January 29, 2005) Hn(1_I%zF  
% uy3<2L#.  
%     Note: if you are using Matlab version 6.x, you may wish to make o1$u;}^|  
%     one or more of the following modifications to this code: 6xJffl  
%       --uncomment line numbers 485 and 486 `**{a/3  
%       --comment out line numbers 552 and 561 <c p
ck  
% vb6EO[e%I  
%*********************************************************************** F1L[3D^-  
clear ?[NC}LC  
%*********************************************************************** ~RuX2u-2&u  
%     Fundamental constants =ZIT!B?4  
%*********************************************************************** NEri{qxm  
cc=2.99792458e8; o"
,8  
muz=4.0*pi*1.0e-7; ^
1bslCe  
epsz=1.0/(cc*cc*muz); j"69uj` R  
etaz=sqrt(muz/epsz); }:ZA)  
%*********************************************************************** .=#jdc/  
%     Material parameters +C{-s  
%*********************************************************************** $Xu3s~:S  
mur=1.0; FHSoj=  
epsr=1.0; UGhEaKH~R  
eta=etaz*sqrt(mur/epsr); _f^KP@^j  
%*********************************************************************** 'YNdrvz  
%     Grid parameters UDg's  
% cZ?QI6|[  
%     Each grid size variable name describes the number of sampled points uD&B{c+a  
%     for a particular field component in the direction of that component. fj5g\m  
%     Additionally, the variable names indicate the region of the grid w#9KtW,tt  
%     for which the dimension is relevant.  For example, ie_tot is the J @"#  
%     number of sample points of Ex along the x-axis in the total P)=.Du)  
%     computational grid, and jh_bc is the number of sample points of Hy p1Zb&:+  
%     along the y-axis in the y-normal UPML regions. /^BC Qaj  
% g8%O^)d=>  
%*********************************************************************** k5.5$<< T  
ie=41;          % Size of main grid nG!<wlY14P  
je=17; U+)p'%f;  
ke=16; -Qn7+?P  
ih=ie+1; :OY~Q3 @  
jh=je+1;   }bjZeh.  
kh=ke+1;   FRrp@hE  
upml=10;        % Thickness of PML boundaries 3N+lWuE}K  
ih_bc=upml+1; \%=\4%:  
jh_bc=upml+1; d7X&3L%Oq  
kh_bc=upml+1; YzI;
)  
ie_tot=ie+2*upml;          % Size of total computational domain 
s
V  
je_tot=je+2*upml;        Lqj Q
v$  
ke_tot=ke+2*upml;        U4pIRa)S  
ih_tot=ie_tot+1; S1
3cQ?4  
jh_tot=je_tot+1;          G:1'}RC :  
kh_tot=ke_tot+1;          }p7iv:P=3  
is=round(ih_tot/2);         % Location of z-directed current source #]@HsVXh7  
js=round(jh_tot/2); d qn5G!fI  
ks=round(ke_tot/2); ~y!'\d>q<  
%*********************************************************************** neDXzMxF  
%     Fundamental grid parameters G:=
hg6'  
%*********************************************************************** (8JU!lin  
delta=0.002; 5G*cAlU  
dt=delta*sqrt(epsr*mur)/(2.0*cc); } p'ZMj&  
nmax=100; %T{]l;5  
%*********************************************************************** H
,!xTy"Wh  
%     Differentiated Gaussian pulse excitation )#}>,,S  
%*********************************************************************** RwWg:4  
rtau=50.0e-12; .gRj^pu   
tau=rtau/dt; _8VP'S=  
ndelay=3*tau; DYD<?._I  
J0=-1.0*epsz; 5~JT*Ny  
%*********************************************************************** `Z?wj@H1`  
%     Initialize field arrays FM@iIlY"  
%*********************************************************************** ~f1g"   
ex=zeros(ie_tot,jh_tot,kh_tot); $RaN@& Wm  
ey=zeros(ih_tot,je_tot,kh_tot); R2~Tr$:  
ez=zeros(ih_tot,jh_tot,ke_tot); u]J@
65~'b  
dx=zeros(ie_tot,jh_tot,kh_tot); `C+<!)2  
dy=zeros(ih_tot,je_tot,kh_tot); |@Tga_0p  
dz=zeros(ih_tot,jh_tot,ke_tot); k&]nF,f
 
hx=zeros(ih_tot,je_tot,ke_tot); 9Yx(u2PQ  
hy=zeros(ie_tot,jh_tot,ke_tot); w )R5P[b  
hz=zeros(ie_tot,je_tot,kh_tot); KQdIG9O+6  
bx=zeros(ih_tot,je_tot,ke_tot); %fqR  
by=zeros(ie_tot,jh_tot,ke_tot); x%G3L\5  
bz=zeros(ie_tot,je_tot,kh_tot); g>@JGzMLP  
%*********************************************************************** pN%&`]Wev  
%     Initialize update coefficient arrays 0M_oFx  
%*********************************************************************** 9t"Rw ns  
C1ex=zeros(size(ex)); 0mY Y:?v  
C2ex=zeros(size(ex)); IU
%|K~_n  
C3ex=zeros(size(ex)); K9lgDk"i  
C4ex=zeros(size(ex)); W(s4R,j  
C5ex=zeros(size(ex)); RdTM5ANT  
C6ex=zeros(size(ex)); aLJm%uW6m&  
C1ey=zeros(size(ey)); yGZsNd {a&  
C2ey=zeros(size(ey)); |"3<\$[  
C3ey=zeros(size(ey)); {m.$EoS  
C4ey=zeros(size(ey)); _!\d?]Ya  
C5ey=zeros(size(ey)); u/zBz*zh  
C6ey=zeros(size(ey)); }{o!  
C1ez=zeros(size(ez)); du3f'=q6|  
C2ez=zeros(size(ez)); \*xB<mq  
C3ez=zeros(size(ez)); ETe4I`d{  
C4ez=zeros(size(ez)); ~&?bU]F  
C5ez=zeros(size(ez)); 'Zfg
Cu)St  
C6ez=zeros(size(ez)); Ey46JO"  
D1hx=zeros(size(hx)); %@/^UE:  
D2hx=zeros(size(hx)); '$K E=Jy  
D3hx=zeros(size(hx)); g`7XE  
D4hx=zeros(size(hx)); "s*-dZO  
D5hx=zeros(size(hx)); #o.e (C  
D6hx=zeros(size(hx)); T~TP  
D1hy=zeros(size(hy)); !>8~R2  
D2hy=zeros(size(hy)); *T|B'80  
D3hy=zeros(size(hy)); -4a9BE".  
D4hy=zeros(size(hy)); #WpkL]g2+%  
D5hy=zeros(size(hy)); Hcq.Lq;2:  
D6hy=zeros(size(hy)); WNjwv/  
D1hz=zeros(size(hz)); 0B NLTRv  
D2hz=zeros(size(hz)); O !L`0 =%c  
D3hz=zeros(size(hz)); P3$eomX'  
D4hz=zeros(size(hz)); Ccf/hA#mb  
D5hz=zeros(size(hz)); &NE e-cb
[  
D6hz=zeros(size(hz)); [VCC+_  
%*********************************************************************** )ZJvx%@i  
%     Update coefficients, as described in Section 7.8.2. ^QB[;g.O  
% Lsmcj{1d  
%     In order to simplify the update equations used in the time-stepping _FLEz|%~  
%     loop, we implement UPML update equations throughout the entire d2 ^}ooE  
%     grid.  In the main grid, the electric-field update coefficients of ;?-AFd\i
 
%     Equations 7.91a-f and the correponding magnetic field update c?p^!zG  
%     coefficients extracted from Equations 7.89 and 7.90 are simplified "/#JC}]  
%     for the main grid (free space) and calculated below. S&op|Z)1  
% ?9b9{c'an  
%*********************************************************************** ]n22+]D  
C1=1.0; xvr5$x|h  
C2=dt; mP(3[a_Q  
C3=1.0; K"}fD;3  
C4=1.0/2.0/epsr/epsr/epsz/epsz; 'Ts:.  
C5=2.0*epsr*epsz; ou|emAV  
C6=2.0*epsr*epsz; /HC:H,"i  
D1=1.0; n/H OP  
D2=dt;  `zwz  
D3=1.0; f-=\qSo  
D4=1.0/2.0/epsr/epsz/mur/muz; H"Pb)t  
D5=2.0*epsr*epsz; 1^p/#jt  
D6=2.0*epsr*epsz; (L_-!=e  
%*********************************************************************** Lpchla$
 
%     Initialize main grid update coefficients iHK~?qd}  
%*********************************************************************** GXNf@&  
C1ex(:,jh_bc:jh_tot-upml,:)=C1;     Zo9<96I&  
C2ex(:,jh_bc:jh_tot-upml,:)=C2; CT|+?  
C3ex(:,:,kh_bc:kh_tot-upml)=C3; US6_5>/  
C4ex(:,:,kh_bc:kh_tot-upml)=C4; PxHFH pL  
C5ex(ih_bc:ie_tot-upml,:,:)=C5; :QCL9QZ'  
C6ex(ih_bc:ie_tot-upml,:,:)=C6; 29R-Up!SVN  
C1ey(:,:,kh_bc:kh_tot-upml)=C1; =P-&dN  
C2ey(:,:,kh_bc:kh_tot-upml)=C2; WeI+|V$  
C3ey(ih_bc:ih_tot-upml,:,:)=C3; XC4Z,,ah"  
C4ey(ih_bc:ih_tot-upml,:,:)=C4; L"L3n,%F  
C5ey(:,jh_bc:je_tot-upml,:)=C5; LSo!_tY  
C6ey(:,jh_bc:je_tot-upml,:)=C6; T5BZD +Ta  
C1ez(ih_bc:ih_tot-upml,:,:)=C1; ::L2zVq5V  
C2ez(ih_bc:ih_tot-upml,:,:)=C2; *dzZOe>,  
C3ez(:,jh_bc:jh_tot-upml,:)=C3; YeX*IZX8  
C4ez(:,jh_bc:jh_tot-upml,:)=C4; B~Q-V&@o  
C5ez(:,:,kh_bc:ke_tot-upml)=C5; +Q*`kg'  
C6ez(:,:,kh_bc:ke_tot-upml)=C6; x%P|T3Qy5  
D1hx(:,jh_bc:je_tot-upml,:)=D1; "(koR Q  
D2hx(:,jh_bc:je_tot-upml,:)=D2; "q4tvcK.  
D3hx(:,:,kh_bc:ke_tot-upml)=D3; e_vsiT  
D4hx(:,:,kh_bc:ke_tot-upml)=D4; "}]`64?  
D5hx(ih_bc:ih_tot-upml,:,:)=D5; adON&<  
D6hx(ih_bc:ih_tot-upml,:,:)=D6; 85{m+1O~  
D1hy(:,:,kh_bc:ke_tot-upml)=D1; 8#I>`z^F  
D2hy(:,:,kh_bc:ke_tot-upml)=D2; GN.Oa$  
D3hy(ih_bc:ie_tot-upml,:,:)=D3; ntiS7g e1  
D4hy(ih_bc:ie_tot-upml,:,:)=D4; ]6&NIz`:,  
D5hy(:,jh_bc:jh_tot-upml,:)=D5; prBLNZp  
D6hy(:,jh_bc:jh_tot-upml,:)=D6; snV*gSUH
 
D1hz(ih_bc:ie_tot-upml,:,:)=D1; 3:%k pnO  
D2hz(ih_bc:ie_tot-upml,:,:)=D2; q>q:ZV  
D3hz(:,jh_bc:je_tot-upml,:)=D3;
9
N]Xa  
D4hz(:,jh_bc:je_tot-upml,:)=D4; <Ox[![SR
 
D5hz(:,:,kh_bc:kh_tot-upml)=D5; ^6 6!f 5^W  
D6hz(:,:,kh_bc:kh_tot-upml)=D6; yoi4w 7:  
%*********************************************************************** k_=SDm a  
%     Fill in PML regions &
4'<{  
% D-3[#~MV  
%     PML theory describes a continuous grading of the material properties <G"cgN#]  
%     over the PML region.  In the FDTD grid it is necessary to discretize )n/%P4l  
%     the grading by averaging the material properties over a grid cell E$d3+``  
%     width centered on each field component.  As an example of the r;cDYg  
%     implementation of this averaging, we take the integral of the A=CeeC]}  
%     continuous sigma(x) in the PML region MatXhP] Fi  
%   #F*|@  
%         sigma_i = integral(sigma(x))/delta xVvUx,t  
%   -!\3;/  
%     where the integral is over a single grid cell width in x, and is qZoDeN-CC  
%     bounded by x1 and x2.  Applying this to the polynomial grading of ]AP1+ &9fN  
%     Equation 7.60a produces w7nt $L5  
% *P()&}JK  
%         sigma_i = (x2^(m+1)-x1^(m+1))*sigmam/(delta*(m+1)*d^m) p:,Y6[gMo  
% yu?5t?vf  
%     where sigmam is the maximum value of sigma as described by Equation C \ Cc[v  
%     7.62. dWY%bb  
%         eh#37*-  
%     The definitions of x1 and x2 depend on the position of the field ffCDO\i({  
%     component within the grid cell.  We have either IS C.~q2  
% 2`yhxO  
%         x1 = (i-0.5)*delta,  x2 = (i+0.5)*delta vNv?trw  
%  We+rFk1ddt  
%     or ]]xKc5CT  
%  H/8^Fvd  
%         x1 = (i)*delta,      x2 = (i+1)*delta rvA>khu0/  
% l=^A41L_  
%     where i varies over the PML region. E(qYCafC  
%  WSThhI  
%*********************************************************************** 61\u{@
o$  
rmax=exp(-16);  %desired reflection error, designated as R(0) in Equation 7.62 <sdgL+&1h  
orderbc=4;      %order of the polynomial grading, designated as m in Equation 7.60a,b A#uU]S  
%   x-varying material properties St=nf\P&F  
delbc=upml*delta; 2FcL-?  
sigmam=-log(rmax)*(orderbc+1.0)/(2.0*eta*delbc); wAMg"ImJ  
sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1.0)); >hKsj{=R7  
kmax=1; T.q2tC[bR  
kfactor=(kmax-1.0)/delta/(orderbc+1.0)/delbc^orderbc; z,HhSW?&^  
for i=1:upml T&U}}iWN  
    SNEhP5!  
    % Coefficients for field components in the center of the grid cell c?::l+  
    x1=(upml-i+1)*delta; B|(g?  
    x2=(upml-i)*delta; owVvbC2<b(  
    sigma=sigfactor*(x1^(orderbc+1)-x2^(orderbc+1)); ,,3lH-C  
    ki=1+kfactor*(x1^(orderbc+1)-x2^(orderbc+1)); 5'lVh/  
    facm=(2*epsr*epsz*ki-sigma*dt); :WhJDx`j  
    facp=(2*epsr*epsz*ki+sigma*dt); ,OZ  
    C5ex(i,:,:)=facp; vwR_2u  
    C5ex(ie_tot-i+1,:,:)=facp; 5
s7BUT  
    C6ex(i,:,:)=facm; r)(5,*v  
    C6ex(ie_tot-i+1,:,:)=facm; ROO*/OOd  
    D1hz(i,:,:)=facm/facp; &|SWy 2N  
    D1hz(ie_tot-i+1,:,:)=facm/facp; rK~-Wz
wu  
    D2hz(i,:,:)=2.0*epsr*epsz*dt/facp; '1<Z"InU
 
    D2hz(ie_tot-i+1,:,:)=2.0*epsr*epsz*dt/facp; N_t,n^i9>*  
    D3hy(i,:,:)=facm/facp; .soCU8i3  
    D3hy(ie_tot-i+1,:,:)=facm/facp; h!"2Ux3!x  
    D4hy(i,:,:)=1.0/facp/mur/muz; M8^ID #  
    D4hy(ie_tot-i+1,:,:)=1.0/facp/mur/muz; jiI=tg;  
    % Coefficients for field components on the grid cell boundary ,"qCz[aDN1  
    x1=(upml-i+1.5)*delta; ~%hdy@  
    x2=(upml-i+0.5)*delta; s"(RdJ-,  
    sigma=sigfactor*(x1^(orderbc+1)-x2^(orderbc+1)); FOaA}D `]  
    ki=1.0+kfactor*(x1^(orderbc+1)-x2^(orderbc+1)); VA/2$5Wu  
    facm=(2.0*epsr*epsz*ki-sigma*dt); #J5BHY~  
    facp=(2.0*epsr*epsz*ki+sigma*dt); !}*N';  
    C1ez(i,:,:)=facm/facp; ~z[`G#dU  
    C1ez(ih_tot-i+1,:,:)=facm/facp; Pz]WT1J0  
    C2ez(i,:,:)=2.0*epsr*epsz*dt/facp; /iW+<@Mas  
    C2ez(ih_tot-i+1,:,:)=2.0*epsr*epsz*dt/facp; 4^_6~YP7  
    C3ey(i,:,:)=facm/facp; 2Gyq40  
    C3ey(ih_tot-i+1,:,:)=facm/facp; lR(9;3  
    C4ey(i,:,:)=1.0/facp/epsr/epsz; >Wg=
Tuef  
    C4ey(ih_tot-i+1,:,:)=1.0/facp/epsr/epsz; e8a^"Z`a  
    D5hx(i,:,:)=facp; :cpj{v;s  
    D5hx(ih_tot-i+1,:,:)=facp; v|?@k^Ms  
    D6hx(i,:,:)=facm; 'Kelq$dn#  
    D6hx(ih_tot-i+1,:,:)=facm; <y 4(!z"  
    G

hM  
end IrwQ~z3I  
%   PEC walls Wzq W1<*`  
C1ez(1,:,:)=-1.0; , 
c.^"5  
C1ez(ih_tot,:,:)=-1.0; p^l#Wq5  
C2ez(1,:,:)=0.0; W5jwD  
C2ez(ih_tot,:,:)=0.0; '.}}k!#  
C3ey(1,:,:)=-1.0; !_glZ*t
L  
C3ey(ih_tot,:,:)=-1.0; B`pBIUu  
C4ey(1,:,:)=0.0; I2}W/}  
C4ey(ih_tot,:,:)=0.0;  /SvhOi  
%   y-varying material properties !E7gIqo  
delbc=upml*delta; w0QtGQ|  
sigmam=-log(rmax)*epsr*epsz*cc*(orderbc+1.0)/(2.0*delbc); 7j& t{q5  
sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1.0)); iAd&o`C  
kmax=1.0; 6]4~]!  
kfactor=(kmax-1.0)/delta/(orderbc+1.0)/delbc^orderbc; ZvY"yl?e  
for j=1:upml b[%@3}E  
    OjU{
r N*  
    % Coefficients for field components in the center of the grid cell .[={Yx0!I  
    y1=(upml-j+1)*delta; vrn4yHoZ  
    y2=(upml-j)*delta; +]
l?JKV  
    sigma=sigfactor*(y1^(orderbc+1)-y2^(orderbc+1)); S)CsH1Q  
    ki=1+kfactor*(y1^(orderbc+1)-y2^(orderbc+1)); t@KTiJI ]  
    facm=(2*epsr*epsz*ki-sigma*dt); cS&KD@.  
    facp=(2*epsr*epsz*ki+sigma*dt); /4{W
T?j  
    VO#rJ
1J  
    C5ey(:,j,:)=facp; h*%p%t<  
    C5ey(:,je_tot-j+1,:)=facp; o.s'0xP]  
    C6ey(:,j,:)=facm; z$^d_)  
    C6ey(:,je_tot-j+1,:)=facm; f5}afPk  
    D1hx(:,j,:)=facm/facp; HOW<IZ^  
    D1hx(:,je_tot-j+1,:)=facm/facp; >}k*!J|  
    D2hx(:,j,:)=2*epsr*epsz*dt/facp; ;R$G.5h  
    D2hx(:,je_tot-j+1,:)=2*epsr*epsz*dt/facp; BRFsw`c  
    D3hz(:,j,:)=facm/facp; |$.?(FZYu  
    D3hz(:,je_tot-j+1,:)=facm/facp; @kXuC<  
    D4hz(:,j,:)=1/facp/mur/muz; 'CBwE&AL  
    D4hz(:,je_tot-j+1,:)=1/facp/mur/muz; +'H[4g`  
    WC_.j^sW  
    % Coefficients for field components on the grid cell boundary o)Q4+njT@  
    y1=(upml-j+1.5)*delta; B'/U#>/  
    y2=(upml-j+0.5)*delta; <O jK $KV  
    sigma=sigfactor*(y1^(orderbc+1)-y2^(orderbc+1)); Y;af|?U*6:  
    ki=1+kfactor*(y1^(orderbc+1)-y2^(orderbc+1)); /Qgb t  
    facm=(2*epsr*epsz*ki-sigma*dt); 3=S|U,  
    facp=(2*epsr*epsz*ki+sigma*dt);    r#-  
     &+9 ;  
    C1ex(:,j,:)=facm/facp; 2[ sY?C  
    C1ex(:,jh_tot-j+1,:)=facm/facp; m:_#kfC&K"  
    C2ex(:,j,:)=2*epsr*epsz*dt/facp; gx\V)8Zr  
    C2ex(:,jh_tot-j+1,:)=2*epsr*epsz*dt/facp; zD_5TGM=  
    C3ez(:,j,:)=facm/facp; * :"*'  
    C3ez(:,jh_tot-j+1,:)=facm/facp; .0Ud?v>=  
    C4ez(:,j,:)=1/facp/epsr/epsz; jAQ{
H  
    C4ez(:,jh_tot-j+1,:)=1/facp/epsr/epsz;   32G
I+NN  
    D5hy(:,j,:)=facp; +|?a7qM  
    D5hy(:,jh_tot-j+1,:)=facp; vc#o(?g  
    D6hy(:,j,:)=facm; +V=<vT
 
    D6hy(:,jh_tot-j+1,:)=facm; Rtf<UhUn  
end @6UY4vq9  
%   PEC walls [*%lm9 x  
C1ex(:,1,:)=-1; +\dVC,,=^g  
C1ex(:,jh_tot,:)=-1; 1N/4W6  
C2ex(:,1,:)=0; R P{pEd  
C2ex(:,jh_tot,:)=0; Owp]>e  
C3ez(:,1,:)=-1; He_O+[sc  
C3ez(:,jh_tot,:)=-1; ?Ld),A/c  
C4ez(:,1,:)=0; 1$Up7=Dr=  
C4ez(:,jh_tot,:)=0;   @`.4"*@M  
%   z-varying material properties v}>g* @  
delbc=upml*delta; at>_EiS  
sigmam=-log(rmax)*epsr*epsz*cc*(orderbc+1)/(2*delbc); aru2H6  
sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1)); zJ`u>:*$  
kmax=1; k?cX fj&  
kfactor=(kmax-1)/delta/(orderbc+1)/delbc^orderbc; lw=kTYbq  
for k=1:upml >iyNZ]."\  
    % Coefficients for field components in the center of the grid cell jMT[+f  
    z1=(upml-k+1)*delta; s'O%@/;J  
    z2=(upml-k)*delta; ~|u;z,\  
    sigma=sigfactor*(z1^(orderbc+1)-z2^(orderbc+1)); l,n_G/\  
    ki=1+kfactor*(z1^(orderbc+1)-z2^(orderbc+1)); V .Kjcy  
    facm=(2*epsr*epsz*ki-sigma*dt); 3qV^RW&  
    facp=(2*epsr*epsz*ki+sigma*dt); t!D
'ZLw
 
    <?7CwW  
    C5ez(:,:,k)=facp; RXRbW%b  
    C5ez(:,:,ke_tot-k+1)=facp; ;5X6`GlS#5  
    C6ez(:,:,k)=facm; GEPWb[Oa  
    C6ez(:,:,ke_tot-k+1)=facm;  ;LS.  
    D1hy(:,:,k)=facm/facp; 74_?@Z(  
    D1hy(:,:,ke_tot-k+1)=facm/facp; m?-)SA  
    D2hy(:,:,k)=2*epsr*epsz*dt/facp; RqROl!6  
    D2hy(:,:,ke_tot-k+1)=2*epsr*epsz*dt/facp; kn#?+Q  
    D3hx(:,:,k)=facm/facp; rEr=Mi2  
    D3hx(:,:,ke_tot-k+1)=facm/facp; Fd8nR9A  
    D4hx(:,:,k)=1/facp/mur/muz; 1@Ba7>%'  
    D4hx(:,:,ke_tot-k+1)=1/facp/mur/muz; h(WlJCln  
    TF%n1H-sF  
    % Coefficients for field components on the grid cell boundary 2e6P?pX~2  
    z1=(upml-k+1.5)*delta; h!B{7J  
    z2=(upml-k+0.5)*delta; Q-)(s  
    sigma=sigfactor*(z1^(orderbc+1)-z2^(orderbc+1)); ^;II@n i  
    ki=1+kfactor*(z1^(orderbc+1)-z2^(orderbc+1)); \^1^|a"  
    facm=(2*epsr*epsz*ki-sigma*dt); $`xpn#lz  
    facp=(2*epsr*epsz*ki+sigma*dt);  hyxv+m[  
    CW`^fI9H  
    C1ey(:,:,k)=facm/facp; k(f),_  
    C1ey(:,:,kh_tot-k+1)=facm/facp; 51:5rN(_  
    C2ey(:,:,k)=2*epsr*epsz*dt/facp; 5|0}bv O  
    C2ey(:,:,kh_tot-k+1)=2*epsr*epsz*dt/facp; R0M>'V?e  
    C3ex(:,:,k)=facm/facp; /{R ^J#  
    C3ex(:,:,kh_tot-k+1)=facm/facp; 8] LF{Obz[  
    C4ex(:,:,k)=1/facp/epsr/epsz; D(z
#)oDr  
    C4ex(:,:,kh_tot-k+1)=1/facp/epsr/epsz; CXUF=IE  
    D5hz(:,:,k)=facp; gd[muR ~  
    D5hz(:,:,kh_tot-k+1)=facp; Vc\
g"1x  
    D6hz(:,:,k)=facm; 4n#u?)  
    D6hz(:,:,kh_tot-k+1)=facm; erI&XI  
end d 6Y9D=O  
%   PEC walls X&Oo[Z  
C1ey(:,:,1)=-1; ?`TQ!m6y  
C1ey(:,:,kh_tot)=-1; fD%/]`y  
C2ey(:,:,1)=0; S5|7D[*  
C2ey(:,:,kh_tot)=0; \m
`IgP*  
C3ex(:,:,1)=-1; yCz"~c  
C3ex(:,:,kh_tot)=-1; QXI~Toddj  
C4ex(:,:,1)=0; 5REH`-  
C4ex(:,:,kh_tot)=0; |A4B4/!  
%figure `&I6=,YLp  
%set(gcf,'DoubleBuffer','on') h5{//0 y  
%*********************************************************************** 1uo
|a  
%     Begin time stepping loop -cUW,>E  
%*********************************************************************** ?;=7{Ej  
for n=1:nmax W3l[a^1d  
    )t~ad]oM  
    % Update magnetic field \Vv)(/q{  
    bstore=bx; CCpRQKb=  
    bx(2:ie_tot,:,:)=D1hx(2:ie_tot,:,:).*  bx(2:ie_tot,:,:)-... l|842N@1  
                     D2hx(2:ie_tot,:,:).*((ez(2:ie_tot,2:jh_tot,:)-ez(2:ie_tot,1:je_tot,:))-... xpZ@DK;  
                                          (ey(2:ie_tot,:,2:kh_tot)-ey(2:ie_tot,:,1:ke_tot)))./delta; ~vP_c(8f  
    hx(2:ie_tot,:,:)= D3hx(2:ie_tot,:,:).*hx(2:ie_tot,:,:)+... }[%F  
                      D4hx(2:ie_tot,:,:).*(D5hx(2:ie_tot,:,:).*bx(2:ie_tot,:,:)-... padV|hF3(e  
                                           D6hx(2:ie_tot,:,:).*bstore(2:ie_tot,:,:)); !,-'wT<v  
    bstore=by; Qfeu3AT  
    by(:,2:je_tot,:)=D1hy(:,2:je_tot,:).*  by(:,2:je_tot,:)-... Gb2|e.z  
                     D2hy(:,2:je_tot,:).*((ex(:,2:je_tot,2:kh_tot)-ex(:,2:je_tot,1:ke_tot))-... x~'_;>]r_  
                                          (ez(2:ih_tot,2:je_tot,:)-ez(1:ie_tot,2:je_tot,:)))./delta; L^u|=9  
    hy(:,2:je_tot,:)= D3hy(:,2:je_tot,:).*hy(:,2:je_tot,:)+... +4J'> dr  
                      D4hy(:,2:je_tot,:).*(D5hy(:,2:je_tot,:).*by(:,2:je_tot,:)-... [voc_o7AI  
                                           D6hy(:,2:je_tot,:).*bstore(:,2:je_tot,:)); Qc33CA  
    bstore=bz; wgDAb#Zuk  
    bz(:,:,2:ke_tot)=D1hz(:,:,2:ke_tot).*  bz(:,:,2:ke_tot)-... A?tCa*b^  
                     D2hz(:,:,2:ke_tot).*((ey(2:ih_tot,:,2:ke_tot)-ey(1:ie_tot,:,2:ke_tot))-... \*PE#RB#6  
                                          (ex(:,2:jh_tot,2:ke_tot)-ex(:,1:je_tot,2:ke_tot)))./delta; ^PdD-t
Y<  
    hz(:,:,2:ke_tot)= D3hz(:,:,2:ke_tot).*hz(:,:,2:ke_tot)+... W}F~vx.  
                      D4hz(:,:,2:ke_tot).*(D5hz(:,:,2:ke_tot).*bz(:,:,2:ke_tot)-... i~GW  
                                           D6hz(:,:,2:ke_tot).*bstore(:,:,2:ke_tot)); H!NGY]z*  
    tzl,r"k3  
    % Update electric field lC*xyOK  
    dstore=dx; 6oKlr,.  
    dx(:,2:je_tot,2:ke_tot)=C1ex(:,2:je_tot,2:ke_tot).*  dx(:,2:je_tot,2:ke_tot)+... 5I*1CIO  
                            C2ex(:,2:je_tot,2:ke_tot).*((hz(:,2:je_tot,2:ke_tot)-hz(:,1:je_tot-1,2:ke_tot))-... -/3h&g  
                                                        (hy(:,2:je_tot,2:ke_tot)-hy(:,2:je_tot,1:ke_tot-1)))./delta; DKo6lP`  
    ex(:,2:je_tot,2:ke_tot)=C3ex(:,2:je_tot,2:ke_tot).*ex(:,2:je_tot,2:ke_tot)+... .aL%}`8l?  
                            C4ex(:,2:je_tot,2:ke_tot).*(C5ex(:,2:je_tot,2:ke_tot).*dx(:,2:je_tot,2:ke_tot)-... @MQfeM-@  
                                                        C6ex(:,2:je_tot,2:ke_tot).*dstore(:,2:je_tot,2:ke_tot)); EQnU:a  
    dstore=dy; Bl)D/  
    dy(2:ie_tot,:,2:ke_tot)=C1ey(2:ie_tot,:,2:ke_tot).*  dy(2:ie_tot,:,2:ke_tot)+... q2k}bb +  
                            C2ey(2:ie_tot,:,2:ke_tot).*((hx(2:ie_tot,:,2:ke_tot)-hx(2:ie_tot,:,1:ke_tot-1))-... };2Lrz9<  
                                                        (hz(2:ie_tot,:,2:ke_tot)-hz(1:ie_tot-1,:,2:ke_tot)))./delta; w2$ L;q  
    ey(2:ie_tot,:,2:ke_tot)=C3ey(2:ie_tot,:,2:ke_tot).*ey(2:ie_tot,:,2:ke_tot)+... "-fyX!  
                            C4ey(2:ie_tot,:,2:ke_tot).*(C5ey(2:ie_tot,:,2:ke_tot).*dy(2:ie_tot,:,2:ke_tot)-... 7|Vpk&.>  
                                                 .. [3irr0D7l  
r<]^.]3zj  

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