[求助]3-D FDTD code with UPML absorbing boundary conditions

%*********************************************************************** Fv| )[>z0  
%     3-D FDTD code with UPML absorbing boundary conditions e7n[NVrX  
%*********************************************************************** !HV<2q()  
% 8)Z)pCN  
%     Program author: Keely J. Willis, Graduate Student f ye=8 r  
%                     UW Computational Electromagnetics Laboratory DlMT<ld  
%                           Director: Susan C. Hagness ;hz;|\ko5  
%                     Department of Electrical and Computer Engineering CyR1.|!@  
%                     University of Wisconsin-Madison jpGZ&L7i&  
%                     1415 Engineering Drive 8^ujA  
%                     Madison, WI 53706-1691 >}"9heF  
%                     kjwillis@wisc.edu >cTSX  
% 0*=[1tdWY  
%     Copyright 2005 >8v4fk IK  
% [w1 4hHnq  
%     This MATLAB M-file implements the finite-difference time-domain {*BZ;Xh\8  
%     solution of Maxwell's curl equations over a three-dimensional n+'gVEBA  
%     Cartesian space lattice comprised of uniform cubic grid cells. 4r+@7hnK  
%     |~+i=y  
%     The dimensions of the computational domain are 8.2 cm j aU.hASj  
%     (x-direction), 3.4 cm (y-direction), and 3.2 cm (z-direction).   [3@Pu.-I+M  
%     The grid is terminated with UPML absorbing boundary conditions. lG1\41ZxB  
% /
/ k`X  
%     An electric current source comprised of two collinear Jz components PLb[U(
~
 
%     (realizing a Hertzian dipole) excites a radially propagating wave.   ro%Jg  
%     The current source is located in the center of the grid.  The _A>?@3La9  
%     source waveform is a differentiated Gaussian pulse given by Iez`g<r  
%          J(t)=J0*(t-t0)*exp(-(t-t0)^2/tau^2), EE{]EW(  
%     where tau=50 ps.  The FWHM spectral bandwidth of this zero-dc- xWiR7~E  
%     content pulse is approximately 7 GHz. The grid resolution rf ?\s/#OY  
%     (dx = 2 mm) was chosen to provide at least 10 samples per mqt$'_M  
%     wavelength up through 15 GHz. NFsCq_f  
% v,[E*qMN  
%     To execute this M-file, type "fdtd3D_UPML" at the MATLAB prompt.   SsY:gp_  
% H Q_IQ+  
%     This code has been tested in the following Matlab environments: e+TSjm  
%     Matlab version 6.1.0.450 Release 12.1 (May 18, 2001) io[>`@=  
%     Matlab version 6.5.1.199709 Release 13 Service Pack 1 (August 4, 2003) (D<_ iV
 
%     Matlab version 7.0.0.19920 R14 (May 6, 2004) pO_$8=G+  
%     Matlab version 7.0.1.24704 R14 Service Pack 1 (September 13, 2004) "mtEjK5  
%     Matlab version 7.0.4.365 R14 Service Pack 2 (January 29, 2005) M:5K4$>Kx  
% l_2B  
%     Note: if you are using Matlab version 6.x, you may wish to make -eQ>3x&3r  
%     one or more of the following modifications to this code: j;7:aM"BQW  
%       --uncomment line numbers 485 and 486 \aY<| 7zK  
%       --comment out line numbers 552 and 561 xlP0?Y1Bl  
% K Y=$RO  
%*********************************************************************** ^b;3Jj  
vWs#4JoG  
clear ` P,-NVB  
O>KrTK-A
V  
%*********************************************************************** j*6>{_[  
%     Fundamental constants kMz*10$gn  
%*********************************************************************** ~WW!P_wI,  
N 4!18{/2  
cc=2.99792458e8; ZL7#44  
muz=4.0*pi*1.0e-7; .7<6 zG6J  
epsz=1.0/(cc*cc*muz); (i1q".  
etaz=sqrt(muz/epsz); ]4X08Cm^  
)wM881_!  
%*********************************************************************** x@p1(V.  
%     Material parameters )8Jf
Bz
R  
%*********************************************************************** ~VKuRli|m  
Hz>_tA"^T  
mur=1.0; {0o,2]o!:  
epsr=1.0; ,SF>$ .  
eta=etaz*sqrt(mur/epsr); gb^<6BYUG  
 d5YL=o  
%*********************************************************************** riu_^!"Z_  
%     Grid parameters 6N#0D2~^  
% oG$OZTc  
%     Each grid size variable name describes the number of sampled points Nf^6t1se  
%     for a particular field component in the direction of that component. @UK%l :L  
%     Additionally, the variable names indicate the region of the grid h`@z61UI  
%     for which the dimension is relevant.  For example, ie_tot is the Oj F]K,$  
%     number of sample points of Ex along the x-axis in the total :#zVF[Y(2  
%     computational grid, and jh_bc is the number of sample points of Hy KKRj#m(:!  
%     along the y-axis in the y-normal UPML regions. ul&}'jBr  
% [W8"Mc|ve  
%*********************************************************************** o]<@E uG  
 oB8LJZ;  
ie=41;          % Size of main grid \hO}3;*&  
je=17; Q>yO,H|  
ke=16; B;A< pNT  
ih=ie+1; }v`Z.?|Z  
jh=je+1;   +v)+ k  
kh=ke+1;   sLOkLz"x  
KX^!t3l6  
upml=10;        % Thickness of PML boundaries Ywo
=w:'  
ih_bc=upml+1; aJzyEb  
jh_bc=upml+1; GTocN1,Z~a  
kh_bc=upml+1; Yma-$ytp  
-d]v6q'1  
ie_tot=ie+2*upml;          % Size of total computational domain #ULzh&yO  
je_tot=je+2*upml;         @#>YU
  
ke_tot=ke+2*upml;         -\[&<o@/D  
ih_tot=ie_tot+1; }I"k=>Ycns  
jh_tot=je_tot+1;           +'"NKZ.>TT  
kh_tot=ke_tot+1;           6sQY)F7p  
6 9s%  
is=round(ih_tot/2);         % Location of z-directed current source \!Wph5wA  
js=round(jh_tot/2); *?x[pqGq  
ks=round(ke_tot/2); 9TUB3x^  
]^6r7nfR6|  
%*********************************************************************** 5@nvcCp  
%     Fundamental grid parameters vWZ?*0^  
%*********************************************************************** 3>#io^35  
hbSXa'
 
delta=0.002; eAK=ylF;  
dt=delta*sqrt(epsr*mur)/(2.0*cc); aE2Yl  
nmax=100; O|mWQp^?q  
QR\2%}9b  
%*********************************************************************** Blox~=cW  
%     Differentiated Gaussian pulse excitation ,K
aO8^PB  
%*********************************************************************** l3Wh&*0  
P_F0lO  
rtau=50.0e-12; +ZJ1> n  
tau=rtau/dt; b\Mb6s  
ndelay=3*tau; G<FB:?|  
J0=-1.0*epsz; Z&6*8#wn  
LJwy,-  
%*********************************************************************** 1#lH5|XQ  
%     Initialize field arrays }Sh3AH/  
%*********************************************************************** G4,.kK  
Y?4N%c_;  
ex=zeros(ie_tot,jh_tot,kh_tot); fD#!0^  
ey=zeros(ih_tot,je_tot,kh_tot); +EvY-mwfQ  
ez=zeros(ih_tot,jh_tot,ke_tot); @^t1SPp  
dx=zeros(ie_tot,jh_tot,kh_tot); THcX.%ToT  
dy=zeros(ih_tot,je_tot,kh_tot); 4CK$W`V  
dz=zeros(ih_tot,jh_tot,ke_tot); Z^t{m!v  
&9khIJIn  
hx=zeros(ih_tot,je_tot,ke_tot); @ [<B:Tqo  
hy=zeros(ie_tot,jh_tot,ke_tot); 4Jk[X>I~  
hz=zeros(ie_tot,je_tot,kh_tot); <y<   
bx=zeros(ih_tot,je_tot,ke_tot); | E\u  
by=zeros(ie_tot,jh_tot,ke_tot); k&pV`.Imi  
bz=zeros(ie_tot,je_tot,kh_tot); 3Lm7{s?=Z-  
3RP\w~?  
%*********************************************************************** 0I}c|V'P  
%     Initialize update coefficient arrays ;6q`c!p7  
%*********************************************************************** mc|8t0+1`  
a\xf\$Ym  
C1ex=zeros(size(ex)); ]owcx=5q%'  
C2ex=zeros(size(ex)); iHk/#a  
C3ex=zeros(size(ex));
,D93A  
C4ex=zeros(size(ex)); |5(un/-C  
C5ex=zeros(size(ex)); Gxw>.O){  
C6ex=zeros(size(ex)); OP98sd&T  
q\d/-K  
C1ey=zeros(size(ey)); ,H@ x.  
C2ey=zeros(size(ey)); $p\0/  
C3ey=zeros(size(ey)); `C)|}qcC  
C4ey=zeros(size(ey)); | W<jN  
C5ey=zeros(size(ey)); r}|a*dh'R  
C6ey=zeros(size(ey)); 9D @}(t!  
]DK.4\^  
C1ez=zeros(size(ez)); XSktbk  
C2ez=zeros(size(ez)); ,L;%-
}#$  
C3ez=zeros(size(ez)); "vo o!&<  
C4ez=zeros(size(ez)); Jyyr'1/<k  
C5ez=zeros(size(ez)); FJIo]p  
C6ez=zeros(size(ez)); '&F PkT:5  
-"x25~k!?F  
D1hx=zeros(size(hx)); >_u5"&q  
D2hx=zeros(size(hx)); Kj6@=  
D3hx=zeros(size(hx)); .t
zQ hd>  
D4hx=zeros(size(hx)); xeKfc}:&z  
D5hx=zeros(size(hx)); qj*77  
D6hx=zeros(size(hx)); 7D=gAMPvJ  
iz:O]kI  
D1hy=zeros(size(hy)); kp8kp
`S7  
D2hy=zeros(size(hy)); 8C
5*:x9l  
D3hy=zeros(size(hy)); xX\A&9m  
D4hy=zeros(size(hy)); ,H5o/qNU`{  
D5hy=zeros(size(hy)); %!V=noo  
D6hy=zeros(size(hy)); ?dQ#%06mn  
^dRgYi"(A  
D1hz=zeros(size(hz)); gjPbhY=C[  
D2hz=zeros(size(hz)); o(Q='kK  
D3hz=zeros(size(hz)); S,GM!YZg  
D4hz=zeros(size(hz)); 7DB!s@"  
D5hz=zeros(size(hz)); ^03M~SNCj  
D6hz=zeros(size(hz)); BF(Kaf;<t.  
)WbE -m  
%*********************************************************************** S!R:a>\  
%     Update coefficients, as described in Section 7.8.2. F=V_ACU  
% D*q:XO6b  
%     In order to simplify the update equations used in the time-stepping ke5_lr(  
%     loop, we implement UPML update equations throughout the entire [OwrIL  
%     grid.  In the main grid, the electric-field update coefficients of ~uweBp~O  
%     Equations 7.91a-f and the correponding magnetic field update Z]k+dJ[-  
%     coefficients extracted from Equations 7.89 and 7.90 are simplified 1*]@1DJ
t  
%     for the main grid (free space) and calculated below. ($s%B  
% ^e:rRk7 &  
%*********************************************************************** 0T<DHPQ1  
3NlG,e'T2  
C1=1.0; r&O:Bt}x  
C2=dt; -3Auo0  
C3=1.0; {p7b\=WB-  
C4=1.0/2.0/epsr/epsr/epsz/epsz; giu8EjzK  
C5=2.0*epsr*epsz; FS6I?q#tQ  
C6=2.0*epsr*epsz; OIrr'uNH  
V6tUijz  
D1=1.0; c3|/8  
D2=dt; -"w&g0Z  
D3=1.0; H >1mi_1  
D4=1.0/2.0/epsr/epsz/mur/muz; ~.TKzh'eB  
D5=2.0*epsr*epsz; Qh,Dcg2ZM"  
D6=2.0*epsr*epsz; 'Q4V(.  
Kz9h{Tu4  
%*********************************************************************** ka[%p,H  
%     Initialize main grid update coefficients 9 p`|~^X  
%*********************************************************************** m95;NT1N/g  
Yf[GpSej  
C1ex(:,jh_bc:jh_tot-upml,:)=C1;     J7$JW3O  
C2ex(:,jh_bc:jh_tot-upml,:)=C2; X{;3gN  
C3ex(:,:,kh_bc:kh_tot-upml)=C3; <dX7{="&  
C4ex(:,:,kh_bc:kh_tot-upml)=C4; 42 &m)  
C5ex(ih_bc:ie_tot-upml,:,:)=C5; 1/vcj~|)t  
C6ex(ih_bc:ie_tot-upml,:,:)=C6; R\>=}7  
uz@WW!+o  
C1ey(:,:,kh_bc:kh_tot-upml)=C1; \ Q0-yNt  
C2ey(:,:,kh_bc:kh_tot-upml)=C2; nISfRXU;  
C3ey(ih_bc:ih_tot-upml,:,:)=C3; m|k:wuzqK  
C4ey(ih_bc:ih_tot-upml,:,:)=C4; ?KXgG'!!  
C5ey(:,jh_bc:je_tot-upml,:)=C5; Tsl0$(2W  
C6ey(:,jh_bc:je_tot-upml,:)=C6; ARa9Ia{@  
!_LRuqQ?"  
C1ez(ih_bc:ih_tot-upml,:,:)=C1; D(^ |'1  
C2ez(ih_bc:ih_tot-upml,:,:)=C2; nY=]KU  
C3ez(:,jh_bc:jh_tot-upml,:)=C3;
5wGc"JHm  
C4ez(:,jh_bc:jh_tot-upml,:)=C4; 6l?\iE  
C5ez(:,:,kh_bc:ke_tot-upml)=C5; @
P xX]e  
C6ez(:,:,kh_bc:ke_tot-upml)=C6; Tp fC  
YLe$Vv735  
D1hx(:,jh_bc:je_tot-upml,:)=D1; h&6t.2<e  
D2hx(:,jh_bc:je_tot-upml,:)=D2; #wL8=QTcNC  
D3hx(:,:,kh_bc:ke_tot-upml)=D3; P] 9-+  
D4hx(:,:,kh_bc:ke_tot-upml)=D4; e(;nhU3a*,  
D5hx(ih_bc:ih_tot-upml,:,:)=D5;
rQ$Jk[Y  
D6hx(ih_bc:ih_tot-upml,:,:)=D6; O{44GB3  
x\!Uk!fM  
D1hy(:,:,kh_bc:ke_tot-upml)=D1; h2fTG  
D2hy(:,:,kh_bc:ke_tot-upml)=D2; gj<Y+Dv>  
D3hy(ih_bc:ie_tot-upml,:,:)=D3; P1}Fn:Xe%7  
D4hy(ih_bc:ie_tot-upml,:,:)=D4; cT,5xp"a  
D5hy(:,jh_bc:jh_tot-upml,:)=D5; ]{E
{ IW8  
D6hy(:,jh_bc:jh_tot-upml,:)=D6; o0Pc^  
S1a}9Z|  
D1hz(ih_bc:ie_tot-upml,:,:)=D1; ]2'{
W]m  
D2hz(ih_bc:ie_tot-upml,:,:)=D2; ,L,?xvWG  
D3hz(:,jh_bc:je_tot-upml,:)=D3; x $=-lB  
D4hz(:,jh_bc:je_tot-upml,:)=D4; a>/jW-?  
D5hz(:,:,kh_bc:kh_tot-upml)=D5; I\oI"\}U  
D6hz(:,:,kh_bc:kh_tot-upml)=D6; *<T,Fyc|  
AHtLkfr(r  
%*********************************************************************** ]WP[hF  
%     Fill in PML regions F` 
gQ[  
% ]Qb85;0)  
%     PML theory describes a continuous grading of the material properties |h75S.UY  
%     over the PML region.  In the FDTD grid it is necessary to discretize *WX,bN6Ot  
%     the grading by averaging the material properties over a grid cell qra5&F
vb  
%     width centered on each field component.  As an example of the >
aV Q  
%     implementation of this averaging, we take the integral of the w`F4.e  
%     continuous sigma(x) in the PML region (vqI@fB';u  
%   SSG}'W!z  
%         sigma_i = integral(sigma(x))/delta lhLE)B2a2  
%   vW:XM0  
%     where the integral is over a single grid cell width in x, and is ~R
\Z&oQ  
%     bounded by x1 and x2.  Applying this to the polynomial grading of }Qo:;&"3  
%     Equation 7.60a produces 4'ymPPY  
% +x"cWOg  
%         sigma_i = (x2^(m+1)-x1^(m+1))*sigmam/(delta*(m+1)*d^m) *C n `pfO  
% (>gAnebN L  
%     where sigmam is the maximum value of sigma as described by Equation En]+mIEo  
%     7.62. ;\N${YIn  
%         om'DaG`A  
%     The definitions of x1 and x2 depend on the position of the field -jOCzp  
%     component within the grid cell.  We have either cWG?`6xU&  
% |UZhMF4/-L  
%         x1 = (i-0.5)*delta,  x2 = (i+0.5)*delta )./
'`Mx?  
%   H3Z"u  
%     or yvz2eAXa  
%   .ko}m{  
%         x1 = (i)*delta,      x2 = (i+1)*delta K,\Bj/V(  
% 9x0Ao*D<t  
%     where i varies over the PML region. -H;p +XAY  
%   ]$gBX=  
%*********************************************************************** @(_M\>!%M  
p4-bD_  
rmax=exp(-16);  %desired reflection error, designated as R(0) in Equation 7.62 `&-)(#  
"O,TL*$  
orderbc=4;      %order of the polynomial grading, designated as m in Equation 7.60a,b yxU??#v|g  
A(
>kp=~  
%   x-varying material properties #`9D,+2iB%  
delbc=upml*delta; ~Q)137u]P  
sigmam=-log(rmax)*(orderbc+1.0)/(2.0*eta*delbc); d9n{jv|  
sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1.0)); L_WVTz?`  
kmax=1; C/L+:b&x~  
kfactor=(kmax-1.0)/delta/(orderbc+1.0)/delbc^orderbc; MGzuQrl{H  
d5ivtK?  
for i=1:upml M&5;Qeoiv  
     ;+/[<bvd"  
    % Coefficients for field components in the center of the grid cell A&~<qgBTp  
    x1=(upml-i+1)*delta; 0Zv<]xO  
    x2=(upml-i)*delta; |2eF~tJqc  
    sigma=sigfactor*(x1^(orderbc+1)-x2^(orderbc+1)); R^=)Ucj  
    ki=1+kfactor*(x1^(orderbc+1)-x2^(orderbc+1)); 0aS&!"o!  
    facm=(2*epsr*epsz*ki-sigma*dt); Lp?JSMe  
    facp=(2*epsr*epsz*ki+sigma*dt); =Nj58l  
L?c7M}vV  
    C5ex(i,:,:)=facp; $2j?Z.yEG  
    C5ex(ie_tot-i+1,:,:)=facp; H _%yh,L  
    C6ex(i,:,:)=facm; .g6DKjy>  
    C6ex(ie_tot-i+1,:,:)=facm; ihrl!A5  
    D1hz(i,:,:)=facm/facp; e~,/Z\i  
    D1hz(ie_tot-i+1,:,:)=facm/facp; !z.C}n5F  
    D2hz(i,:,:)=2.0*epsr*epsz*dt/facp;
Py)'%e  
    D2hz(ie_tot-i+1,:,:)=2.0*epsr*epsz*dt/facp; {} 11U0  
    D3hy(i,:,:)=facm/facp; @94_'i7\  
    D3hy(ie_tot-i+1,:,:)=facm/facp; =_/,C  
    D4hy(i,:,:)=1.0/facp/mur/muz; 
`xpU  
    D4hy(ie_tot-i+1,:,:)=1.0/facp/mur/muz; 5c~OG6COx  
Tpv]c  
    % Coefficients for field components on the grid cell boundary pWwB<F  
    x1=(upml-i+1.5)*delta; =5-|H;da  
    x2=(upml-i+0.5)*delta; ages-Z_X  
    sigma=sigfactor*(x1^(orderbc+1)-x2^(orderbc+1)); !MiH^wP  
    ki=1.0+kfactor*(x1^(orderbc+1)-x2^(orderbc+1)); 4l~0LdYXKm  
    facm=(2.0*epsr*epsz*ki-sigma*dt); 8I'Am"bc\  
    facp=(2.0*epsr*epsz*ki+sigma*dt); LFx*_3a  
mfNYN4Um6  
    C1ez(i,:,:)=facm/facp; H8}}R~ZO  
    C1ez(ih_tot-i+1,:,:)=facm/facp; )@]Y1r4U  
    C2ez(i,:,:)=2.0*epsr*epsz*dt/facp; j`9+pI  
    C2ez(ih_tot-i+1,:,:)=2.0*epsr*epsz*dt/facp; +I+7@XiZ  
    C3ey(i,:,:)=facm/facp; +'NiuN  
    C3ey(ih_tot-i+1,:,:)=facm/facp; Gv};mkX[N  
    C4ey(i,:,:)=1.0/facp/epsr/epsz; "c S?t  
    C4ey(ih_tot-i+1,:,:)=1.0/facp/epsr/epsz; }m~2[5q%/  
    D5hx(i,:,:)=facp; lTh}0t  
    D5hx(ih_tot-i+1,:,:)=facp; 'e(`
2  
    D6hx(i,:,:)=facm; -Oro$=%  
    D6hx(ih_tot-i+1,:,:)=facm; P|S'MS';:  
     mj{/'  
end I=,u7w`m  
2_4m}T3  
%   PEC walls e8TJ =}\  
C1ez(1,:,:)=-1.0; 2@(Qd3N(  
C1ez(ih_tot,:,:)=-1.0; W~1MeAI  
C2ez(1,:,:)=0.0; _/)?GXwLn  
C2ez(ih_tot,:,:)=0.0; sH>Z{xjr  
C3ey(1,:,:)=-1.0; nFn@Z'T$N  
C3ey(ih_tot,:,:)=-1.0; `euk&]/^.)  
C4ey(1,:,:)=0.0; kXq*Jq  
C4ey(ih_tot,:,:)=0.0; Q\DD^Pbq  
T&2aNkuG  
%   y-varying material properties Wkk=x&  
delbc=upml*delta; A~!3svJW  
sigmam=-log(rmax)*epsr*epsz*cc*(orderbc+1.0)/(2.0*delbc); '42P=vzo  
sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1.0)); U-$ B"w&  
kmax=1.0; ?'_Q^O>  
kfactor=(kmax-1.0)/delta/(orderbc+1.0)/delbc^orderbc; hupYiI~  
#egP*{F   
for j=1:upml # Z*nc0C  
     h%Nbx:vKk  
    % Coefficients for field components in the center of the grid cell "/)}Cc,L  
    y1=(upml-j+1)*delta; hal3J  
    y2=(upml-j)*delta; S|8O$9{x9q  
    sigma=sigfactor*(y1^(orderbc+1)-y2^(orderbc+1)); o'3t(dyyH  
    ki=1+kfactor*(y1^(orderbc+1)-y2^(orderbc+1)); H:ar&o#(  
    facm=(2*epsr*epsz*ki-sigma*dt); xpf\S10e  
    facp=(2*epsr*epsz*ki+sigma*dt); J!@$lyH  
     6c3+q+#J2  
    C5ey(:,j,:)=facp; &S.zc@rN  
    C5ey(:,je_tot-j+1,:)=facp; eKL)jzC:  
    C6ey(:,j,:)=facm; $h Isab_  
    C6ey(:,je_tot-j+1,:)=facm; 5O9Oi:-!c  
    D1hx(:,j,:)=facm/facp; I499Rrw#E  
    D1hx(:,je_tot-j+1,:)=facm/facp; h<wF;g,  
    D2hx(:,j,:)=2*epsr*epsz*dt/facp; *q%)q  
    D2hx(:,je_tot-j+1,:)=2*epsr*epsz*dt/facp; G}tq'#]E{z  
    D3hz(:,j,:)=facm/facp; RoXU>a:nS  
    D3hz(:,je_tot-j+1,:)=facm/facp; VK+#!!Ha  
    D4hz(:,j,:)=1/facp/mur/muz; 4:=eO!6  
    D4hz(:,je_tot-j+1,:)=1/facp/mur/muz; ~67L  
     MK]S205{  
    % Coefficients for field components on the grid cell boundary 5@+8*Fdk  
    y1=(upml-j+1.5)*delta; ]3iu-~  
    y2=(upml-j+0.5)*delta; W`C&$v#  
    sigma=sigfactor*(y1^(orderbc+1)-y2^(orderbc+1)); h-1eDxK6  
    ki=1+kfactor*(y1^(orderbc+1)-y2^(orderbc+1)); 89B1\ff  
    facm=(2*epsr*epsz*ki-sigma*dt); >sE5zj|V  
    facp=(2*epsr*epsz*ki+sigma*dt);     K/ q:aMq  
     '\:?FQ C  
    C1ex(:,j,:)=facm/facp; ;a+>><x]  
    C1ex(:,jh_tot-j+1,:)=facm/facp; Fc;)p88[  
    C2ex(:,j,:)=2*epsr*epsz*dt/facp; <d
To-P  
    C2ex(:,jh_tot-j+1,:)=2*epsr*epsz*dt/facp; K%<Z"2!+  
    C3ez(:,j,:)=facm/facp; ^Slwg|t*~P  
    C3ez(:,jh_tot-j+1,:)=facm/facp; 3ySP*J5  
    C4ez(:,j,:)=1/facp/epsr/epsz; j.GpJDq  
    C4ez(:,jh_tot-j+1,:)=1/facp/epsr/epsz;   |5}{4k~9J  
    D5hy(:,j,:)=facp; ~>@Dn40  
    D5hy(:,jh_tot-j+1,:)=facp; n_@YKz;8  
    D6hy(:,j,:)=facm; n8zh;vuJ  
    D6hy(:,jh_tot-j+1,:)=facm; '|e5cW6z  
jZ<
*XX  
end BZqb o`9  
x C'>W"pY  
%   PEC walls =>6Z"LD(  
C1ex(:,1,:)=-1; }6P]32d  
C1ex(:,jh_tot,:)=-1; 'M\ou}P  
C2ex(:,1,:)=0; DTdL|x.{  
C2ex(:,jh_tot,:)=0; $S$%avRX  
C3ez(:,1,:)=-1; BCya5!uy  
C3ez(:,jh_tot,:)=-1; zxCxGT\;  
C4ez(:,1,:)=0; G}<q  
C4ez(:,jh_tot,:)=0;   V#W(c_g
 
B@]( ,  
%   z-varying material properties %ma1LN[  
delbc=upml*delta; R Nr=M^Zn  
sigmam=-log(rmax)*epsr*epsz*cc*(orderbc+1)/(2*delbc); E'LkoyI  
sigfactor=sigmam/(delta*(delbc^orderbc)*(orderbc+1)); #(@dN+  
kmax=1; t-SG
G{  
kfactor=(kmax-1)/delta/(orderbc+1)/delbc^orderbc; :L9\`&}FS  
VGBL<X  
for k=1:upml EX8:B.z`57  
J#CF SG
  
    % Coefficients for field components in the center of the grid cell R|{6JsjG10  
    z1=(upml-k+1)*delta; au8bEw&W  
    z2=(upml-k)*delta; &^thKXEC  
    sigma=sigfactor*(z1^(orderbc+1)-z2^(orderbc+1)); n<7#?X7  
    ki=1+kfactor*(z1^(orderbc+1)-z2^(orderbc+1)); WK#lE&V3  
    facm=(2*epsr*epsz*ki-sigma*dt); uH]n/Kv1,  
    facp=(2*epsr*epsz*ki+sigma*dt); =,I,K=+_x  
     ;w?zmj<Dm  
    C5ez(:,:,k)=facp; kX{c+qHM  
    C5ez(:,:,ke_tot-k+1)=facp; U %Aj~K^b  
    C6ez(:,:,k)=facm; 4qjY,QJ  
    C6ez(:,:,ke_tot-k+1)=facm; tkWWR%c"  
    D1hy(:,:,k)=facm/facp; <;x+?j  
    D1hy(:,:,ke_tot-k+1)=facm/facp; KhZ'Ic[vw  
    D2hy(:,:,k)=2*epsr*epsz*dt/facp; ~
s{$&N  
    D2hy(:,:,ke_tot-k+1)=2*epsr*epsz*dt/facp; +bd/*^  
    D3hx(:,:,k)=facm/facp; R+Ke|C  
    D3hx(:,:,ke_tot-k+1)=facm/facp; !.iA^D//]  
    D4hx(:,:,k)=1/facp/mur/muz; "P< drz<  
    D4hx(:,:,ke_tot-k+1)=1/facp/mur/muz; }6eWdm!B  
     J?5O2n  
    % Coefficients for field components on the grid cell boundary |mrAvm}  
    z1=(upml-k+1.5)*delta; E/_=0t  
    z2=(upml-k+0.5)*delta; c*!bT$]~\  
    sigma=sigfactor*(z1^(orderbc+1)-z2^(orderbc+1)); f7XmVCz1  
    ki=1+kfactor*(z1^(orderbc+1)-z2^(orderbc+1)); <acAc2  
    facm=(2*epsr*epsz*ki-sigma*dt); FFtj5e  
    facp=(2*epsr*epsz*ki+sigma*dt); kaUH#;c>_  
     [HIg\N$I8C  
    C1ey(:,:,k)=facm/facp; 0;e>kz3o  
    C1ey(:,:,kh_tot-k+1)=facm/facp; G <m{o  
    C2ey(:,:,k)=2*epsr*epsz*dt/facp; &&[j/d}J  
    C2ey(:,:,kh_tot-k+1)=2*epsr*epsz*dt/facp; xJ%b<y{@  
    C3ex(:,:,k)=facm/facp; dvsOJj/b  
    C3ex(:,:,kh_tot-k+1)=facm/facp; a+*|P  
    C4ex(:,:,k)=1/facp/epsr/epsz;  ~J"*ahl  
    C4ex(:,:,kh_tot-k+1)=1/facp/epsr/epsz; yA(H=L-=!1  
    D5hz(:,:,k)=facp; %
Q}#x  
    D5hz(:,:,kh_tot-k+1)=facp; <s-_ieW'  
    D6hz(:,:,k)=facm; O>w
$  
    D6hz(:,:,kh_tot-k+1)=facm; LP_!g  
=bf-+gZD  
end >'Nrvy%&0  
)T?w,"kI  
%   PEC walls 9ZG.%+l  
%C1ey(:,:,1)=-1; NK*~UePy  
%C1ey(:,:,kh_tot)=-1; $K\\8$Z  
C2ey(:,:,1)=0; \rADwZm  
C2ey(:,:,kh_tot)=0;  7P]_03  
C3ex(:,:,1)=-1; Old5E&  
C3ex(:,:,kh_tot)=-1; y{K~g<VL  
C4ex(:,:,1)=0; =g/K>B  
C4ex(:,:,kh_tot)=0; .he%a3e  
 2c!?!:s  
%figure 34]f[jJ|  
%set(gcf,'DoubleBuffer','on') ^l_W9s  
I2|iqbX40Q  
%*********************************************************************** /5
suyM=U  
%     Begin time stepping loop "S#0QH%5  
%*********************************************************************** {Ca#{LeLk  
sKjg)3Sl  
for n=1:nmax ykl./uY'  
     ksm=<I"C  
    % Update magnetic field E'Egc4Z2=l  
    bstore=bx; ^5u}   
    bx(2:ie_tot,:,:)=D1hx(2:ie_tot,:,:).*  bx(2:ie_tot,:,:)-...  *;+lF  
                     D2hx(2:ie_tot,:,:).*((ez(2:ie_tot,2:jh_tot,:)-ez(2:ie_tot,1:je_tot,:))-... w{K_+}fAC  
                                          (ey(2:ie_tot,:,2:kh_tot)-ey(2:ie_tot,:,1:ke_tot)))./delta; jbC7U9t7  
    hx(2:ie_tot,:,:)= D3hx(2:ie_tot,:,:).*hx(2:ie_tot,:,:)+... )e9(&y*o  
                      D4hx(2:ie_tot,:,:).*(D5hx(2:ie_tot,:,:).*bx(2:ie_tot,:,:)-... |,t#Au}61  
                                           D6hx(2:ie_tot,:,:).*bstore(2:ie_tot,:,:)); &hd+x5  
    bstore=by; R$(,~~MH  
    by(:,2:je_tot,:)=D1hy(:,2:je_tot,:).*  by(:,2:je_tot,:)-... Z'WoChjM  
                     D2hy(:,2:je_tot,:).*((ex(:,2:je_tot,2:kh_tot)-ex(:,2:je_tot,1:ke_tot))-... |;{wy  
                                          (ez(2:ih_tot,2:je_tot,:)-ez(1:ie_tot,2:je_tot,:)))./delta; ]t7<$L   
    hy(:,2:je_tot,:)= D3hy(:,2:je_tot,:).*hy(:,2:je_tot,:)+... u;~/B[  
                      D4hy(:,2:je_tot,:).*(D5hy(:,2:je_tot,:).*by(:,2:je_tot,:)-... 1>57rx"l  
                                           D6hy(:,2:je_tot,:).*bstore(:,2:je_tot,:)); X,x{!  
    bstore=bz; !K(0)~u  
    bz(:,:,2:ke_tot)=D1hz(:,:,2:ke_tot).*  bz(:,:,2:ke_tot)-... T\8|Q@  
                     D2hz(:,:,2:ke_tot).*((ey(2:ih_tot,:,2:ke_tot)-ey(1:ie_tot,:,2:ke_tot))-... y| @[?B  
                                          (ex(:,2:jh_tot,2:ke_tot)-ex(:,1:je_tot,2:ke_tot)))./delta; %S.R@C[3  
    hz(:,:,2:ke_tot)= D3hz(:,:,2:ke_tot).*hz(:,:,2:ke_tot)+... b
V;R}3)  
                      D4hz(:,:,2:ke_tot).*(D5hz(:,:,2:ke_tot).*bz(:,:,2:ke_tot)-... $+S'Boo  
                                           D6hz(:,:,2:ke_tot).*bstore(:,:,2:ke_tot)); 6!Ji-'\"  
     im%'S6_X4  
    % Update electric field &bs/a]?Z7  
    dstore=dx;  $C(}  
    dx(:,2:je_tot,2:ke_tot)=C1ex(:,2:je_tot,2:ke_tot).*  dx(:,2:je_tot,2:ke_tot)+... C#>c(-p>RC  
                            C2ex(:,2:je_tot,2:ke_tot).*((hz(:,2:je_tot,2:ke_tot)-hz(:,1:je_tot-1,2:ke_tot))-... "+&|$*  
                                                        (hy(:,2:je_tot,2:ke_tot)-hy(:,2:je_tot,1:ke_tot-1)))./delta; +UHf&i/3
 
    ex(:,2:je_tot,2:ke_tot)=C3ex(:,2:je_tot,2:ke_tot).*ex(:,2:je_tot,2:ke_tot)+... 0l^-[jK)  
                            C4ex(:,2:je_tot,2:ke_tot).*(C5ex(:,2:je_tot,2:ke_tot).*dx(:,2:je_tot,2:ke_tot)-... aQ]C`9k  
                                                        C6ex(:,2:je_tot,2:ke_tot).*dstore(:,2:je_tot,2:ke_tot)); WK/Byd.Z  
    dstore=dy; `<y2l94tL  
    dy(2:ie_tot,:,2:ke_tot)=C1ey(2:ie_tot,:,2:ke_tot).*  dy(2:ie_tot,:,2:ke_tot)+... $0D]d.w=  
                            C2ey(2:ie_tot,:,2:ke_tot).*((hx(2:ie_tot,:,2:ke_tot)-hx(2:ie_tot,:,1:ke_tot-1))-... R(r89bTQ  
                                                        (hz(2:ie_tot,:,2:ke_tot)-hz(1:ie_tot-1,:,2:ke_tot)))./delta; E;D9S  
    ey(2:ie_tot,:,2:ke_tot)=C3ey(2:ie_tot,:,2:ke_tot).*ey(2:ie_tot,:,2:ke_tot)+... O)`R)MQ)  
                            C4ey(2:ie_tot,:,2:ke_tot).*(C5ey(2:ie_tot,:,2:ke_tot).*dy(2:ie_tot,:,2:ke_tot)-... yWFDGk  
                                                        C6ey(2:ie_tot,:,2:ke_tot).*dstore(2:ie_tot,:,2:ke_tot)); ph%/;?wY  
    dstore=dz; XLg6?Nu  
    dz(2:i .. QF'N8Kla  
1/6G&RB  

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在代码里找 PEC WALL，系数的定义，决定边界E场为0。

这里的PEC边界不需要在迭代公式里写，因为不需要更新边界上的场    设置了PEC边界后   在后边的迭代自动产生作用   注意迭代的起止坐标 =MDir$1Z  
[tsi8r=T  
新手  请指教

这个程序的吸收效果好吗？调试了下好像吸收效果不怎么好？

谢谢分享啊