FDTD算法的Matlab程序

1、%* 5= T$h;O % 3-D FDTD code with PEC boundaries Iw?*y.z| %* H!4A& % r dCs % Program author: Susan C. Hagness B_?7+ % Department of Electrical and Computer Engineering &hrMpD6z6i % University of Wisconsin-Madison T/|nOu 5 % 1415 Engineering Drive 41P0)o % Madison, WI 53706-1691 9MH;=88q % 608-265-573

2、9 :s zkh? % |UA=? Xl % )_;l%& % Date of this version: February 2000 !$Ivro % yYSmmgrX0 % This MATLAB M-file implements the finite-difference time-domain (F$r$9S % solution of Maxwells curl equations over a three-dimensional $gN%X/n1 % Cartesian space lattice comprised of uniform

3、 cubic grid cells. %hN(79:g % vq.o ;q / % To illustrate the algorithm, an air-filled rectangular cavity Gy+- % conditions: yUDoOVC0 % ex(i,j,k)=0 on the j=1, j=jb, k=1, and k=kb planes kyN) % ey(i,j,k)=0 on the i=1, i=ib, k=1, and k=kb planes 7Hv 6z#m % ez(i,j,k)=0 on the i=1, i=ib, j=1, and j=jb pl

4、anes 9, % These PEC boundaries form the outer lossless walls of the cavity. A6z.MdYZ % a&qdp % The cavity is excited by an additive current source oriented x 9 a % along the z-direction. The source waveform is a differentiated Qj1%wWG % Gaussian pulse given by #K!jh)y % J(t)=-J0*(t-t0)*exp(-(t-t0)2/

5、tau2), dMjeF % where tau=50 ps. The FWHM spectral bandwidth of this zero-dc- eYoc(bG(+ % content pulse is approximately 7 GHz. The grid resolution Gs|a$ V|o % (dx = 2 mm) was chosen to provide at least 10 samples per j1;0kb? % wavelength up through 15 GHz. jqjj2 9 % _XV , p % To execute this M-file,

6、 type fdtd3D at the MATLAB prompt. g(sR ? % This M-file displays the FDTD-computed Ez fields at every other Wt!;Y,1 s % time step, and records those frames in a movie matrix, M, which i WGGnGS % is played at the end of the simulation using the movie command. WTt /y6 % j+/EG*/ %* cMy?& _3f/lG?&- clea

7、r EOqV5$+ czWUD %* ov!L8 9u % Fundamental constants Tgq,tR %* _bGV d +eb!fi cc=2.e8; %speed of light in free space Di_K muz=4.0*pi*1.0e-7; %permeability of free space lPHeO+M ?nR$a %* $:DhK % Grid parameters .7#04_aP %* jRjQDK_ka (?l ke=10; %number of grid cells in z-direction Aa%ks+1 s0Xihsw6 ib=ie

8、+1; gB#$mq, jb=je+1; D#&N? kb=ke+1; iW B1dp YJrZ is=26; %location of z-directed current source +xtRY js=13; %location of z-directed current source LaiUf_W#X XW kobs=5; El6?ml 47XQZ-4 dx=0.002; %space increment of cubic lattice jZ3 dt=dx/(2.0*cc); %time step N XzgI SuW_6 nmax=500; %total number of ti

9、me steps # 1,(I ghiFIACMO %* dYJWQ;j.| F/PN1#T rtau=50.0e-12; |k _ jO tau=rtau/dt; y_8 8I:O ndelay=3*tau; /W/ =OPe srcconst=-dt*3.0e+11; mg*,_3q33 6546sU %* %Sfew/R0 % Material parameters qI PI!s %* C jsy1gA FU Ip eps=1.0; 3xhxE sig=0.0; 5R/!e(m r+;op_ %* :v&TQ % Updating coefficients iu2%S)w %* SS1

10、-UbL qJ8V cb=(dt/epsz/eps/dx)/(1.0+(dt*sig)/(2.0*epsz*eps); ?k?7GN da=1.0; +dcB h Dq db=dt/muz/dx; #TM+Vd$ f JY %* -uXf?sTV % Field arrays ra/5D %* $014/IB fb.jXSR ex=zeros(ie,jb,kb); eW, E)x: ey=zeros(ib,je,kb); bfcQ( m5 ez=zeros(ib,jb,ke); ul$k xc=N hx=zeros(ib,je,ke); W%5o87 hy=zeros(ie,jb,ke); q

11、#B=PZNA hz=zeros(ie,je,kb); Z;Q2tT /F OSreS5bg %* +Ch2Lod % Movie initialization C.qN Bl* %* .n$c+ O0m_ tview(:,:)=ez(:,:,kobs); elF#$ sview(:,:)=ez(:,js,:); B xAyjA6 |5il5UP subplot(position,0.15 0.45 0.7 0.45),pcolor(tview); +_EE shading flat; mH:8_=(. *is(-1.0 1.0); 6roq 1= colorbar; ,GeW_!Q axis

12、 image; Ms shading flat; :3N6Ej *is(-1.0 1.0); ajCe&+ colorbar; %E8HLTEvl axis image; E | title(Ez(i,j=13,k), time step = 0); qWU59:d xlabel(i coordinate); 3qQU-;| ylabel(k coordinate); zr 4JTS 9=J 3T66U rect=get(gcf,Position); qEH rect(1:2)=0 0; # uyAC$ )j QrD M=moviein(nmax/2,gcf,rect); DUmp6 X2zI

13、Fm %* _gfec4o % BEGIN TIME-STEPPING LOOP Z= LLL %* uF ;8B P_Pco for n=1:nmax rM4RibS 5Z(q|nn7P %* uG+eF % Update electric fields pf#R %* + jN)$Y3Ya x f)P ex(1:ie,2:je,2:ke)=ca*ex(1:ie,2:je,2:ke)+. J,IxRGi cb*(hz(1:ie,2:je,2:ke)-hz(1:ie,1:je-1,2:ke)+. Pk8(2fAYk hy(1:ie,2:je,1:ke-1)-hy(1:ie,2:je,2:ke)

14、; ()fYhk|W ? !#1 ey(2:ie,1:je,2:ke)=ca*ey(2:ie,1:je,2:ke)+. C?rb(m cb*(hx(2:ie,1:je,2:ke)-hx(2:ie,1:je,1:ke-1)+. 1 y7$N8Xo hz(1:ie-1,1:je,2:ke)-hz(2:ie,1:je,2:ke); d 8z9_C- IQB%v5 ez(2:ie,2:je,1:ke)=ca*ez(2:ie,2:je,1:ke)+. fMg+X cb*(hx(2:ie,1:je-1,1:ke)-hx(2:ie,2:je,1:ke)+. r+n hm9 hy(2:ie,2:je,1:ke

15、)-hy(1:ie-1,2:je,1:ke); h_7Dn rgu7g ez(is,js,1:ke)=ez(is,js,1:ke)+. pJETM srcconst*(n-ndelay)*exp(-(n-ndelay)2/tau2); -PH qD j, % Update magnetic fields o(5 ( bJ %* o n?8l?iQ ?;Ge/QU5 hx(2:ie,1:je,1:ke)=hx(2:ie,1:je,1:ke)+. ,:/3L db*(ey(2:ie,1:je,2:kb)-ey(2:ie,1:je,1:ke)+. .Ue1v*, ez(2:ie,1:je,1:ke)

16、-ez(2:ie,2:jb,1:ke); 2o-Ie/d m_1BB$lyP2 hy(1:ie,2:je,1:ke)=hy(1:ie,2:je,1:ke)+. AqPQeNgz db*(ex(1:ie,2:je,1:ke)-ex(1:ie,2:je,2:kb)+. u:D,;) ez(2:ib,2:je,1:ke)-ez(1:ie,2:je,1:ke); Sf*b6lcC WT2eMK hz(1:ie,1:je,2:ke)=hz(1:ie,1:je,2:ke)+. QWV12t$v db*(ex(1:ie,2:jb,2:ke)-ex(1:ie,1:je,2:ke)+. z/Yrf ey(1:i

17、e,1:je,2:ke)-ey(2:ib,1:je,2:ke); =%V(n7= FY.my8 %* 6vQCghI % Visualize fields gK8=A0c %* A7qKY-4B HYf if mod(n,2)=0; $Dm2:Dmt plRBfwN timestep=int2str(n); BB694 tview(:,:)=ez(:,:,kobs); :d ts sview(:,:)=ez(:,js,:); *+qlam4N vPDF+u subplot(position,0.15 0.45 0.7 0.45),pcolor(tview); u._B7R& shading flat; W/3,vf1 *is(-1.0 1.0); gxIGL-1M colorbar; 5*ip