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1、精選優(yōu)質(zhì)文檔-傾情為你奉上%* 5= T$h;O % 3-D FDTD code with PEC boundaries Iw?*y.z| %* H!'4A& % r dCs % Program author: Susan C. Hagness B_?7+ % Department of Electrical and Compute
2、r Engineering &hrMpD6z6i % University of Wisconsin-Madison T/|nOu 5 % 1415 Engineering Drive 41P0)o %
3、0; Madison, WI 53706-1691 9MH;=88q % 608-265-5739 :s zkh? % |UA=? Xl % )_;l%& % Date of this
4、version: February 2000 !$Ivro % yYSmmgrX0 % This MATLAB M-file implements the finite-difference time-domain ("F$r$9S % solution of Maxwell's curl equations over a three-dimensional $gN%X/n"1 % Cartesian space lattice
5、comprised of uniform cubic grid cells. %hN(79:g % vq.o ;q / % To illustrate the algorithm, an air-filled rectangular cavity < Np Mv!g % resonator is modeled. The length, width, and height of the pojhfn % cavity are 10.0 cm (x-di
6、rection), 4.8 cm (y-direction), and VcXr!4 M % 2.0 cm (z-direction), respectively. DU81( % #pgD-0_ % The computational domain is truncated using PEC boundary >Gy+- % conditions: yUDoOVC0 % ex(i,
7、j,k)=0 on the j=1, j=jb, k=1, and k=kb planes kyN) % ey(i,j,k)=0 on the i=1, i=ib, k=1, and k=kb planes 7Hv 6>z#m % ez(i,j,k)=0 on the i=1, i=ib, j=1, and j=jb planes <9"<, % These PEC bo
8、undaries form the outer lossless walls of the cavity. A6z.MdYZ % a&qdp % The cavity is excited by an additive current source oriented x 9 a % along the z-direction. The source waveform is a differentiated Qj1%'wWG % Gaussia
9、n pulse given by #K!jh)y % J(t)=-J0*(t-t0)*exp(-(t-t0)2/tau2), dMjeF % where tau=50 ps. The FWHM spectral bandwidth of this zero-dc- eYoc(bG(+ % content pulse is approximately 7 GHz. The grid resolution Gs|a$ V|o
10、60;% (dx = 2 mm) was chosen to provide at least 10 samples per j1;0kb? % wavelength up through 15 GHz. jqjj2 9 % _X<V , p % To execute this M-file, type "fdtd3D" at the MATLAB prompt. g(sR ? % This M-file displa
11、ys 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 /y'6 % j+/EG*/ %* cMy?&
12、;_3f/lG?&- clear EOqV5$+ czWUD %* ov!L8 9u % Fundamental constants Tgq,tR %* <_bGV d +eb!fi cc=2.e8; %speed of light in free space Di_K muz=4.0*pi*1.0e-7; %p
13、ermeability of free space <lPHeO< epsz=1.0/(cc*cc*muz); %permittivity of free space c/3M>+M ?nR$>a %* $:DhK % Grid parameters .7#04_aP %* jRjQDK_"ka (<G) +* ie=50; %number of grid cells
14、 in x-direction pQ+4+7ID je=24; %number of grid cells in y-direction L30>?l ke=10; %number of grid cells in z-direction Aa%ks+1 s0'Xihsw6 ib=ie+1; gB#$"mq, jb=je+1; D#&N?< kb=ke+1; iW <B1'dp Y
15、JrZ is=26; %location of z-directed current source +xtRY" js=13; %location of z-directed current source LaiUf_W#X X<"W kobs=5; <El6?ml 47XQZ-4 dx=0.002; %space increment of cu
16、bic lattice jZ3 dt=dx/(2.0*cc); %time step N XzgI SuW_6 nmax=500; %total number of time steps # 1,(I ghiFI<)VY cF aYI %* /Et:',D % Differentiated Gaussian pulse excitation >ACMO %* d
17、YJWQ;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 6546"sU %* %Sfew/"R0 % Material parameters qI" PI!s %* C jsy1gA FU Ip eps=1.0; 3xhxE
18、 sig=0.0; 5R/!e(m r+;op_ %* :v&TQ % Updating coefficients iu2%S)w %* SS1-UbL q<yp6Q3 ca=(1.0-(dt*sig)/(2.0*epsz*eps)/(1.0+(dt*sig)/(2.0*epsz*eps); AF>J8V cb=(dt/epsz/eps/dx)/(1.0+(dt*sig)/(2.0*epsz*eps); ?k?7GN da=1.0; +dcB
19、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)
20、; q#B=PZ'NA 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 0.4
21、5),pcolor(tview'); +_EE shading flat; mH:8_=(. *is(-1.0 1.0); 6roq 1= colorbar; ,GeW_!Q axis image; Ms<v81z5T title('Ez(i,j,k=5), time step = 0'); Jb/VITqN4 xlabel('i coordinate'); pTB1I3=.u ylabel('j coordinate'); c1tM(& &
22、#160;5J-slNNCQ subplot('position',0.15 0.10 0.7 0.25),pcolor(sview'); Mz&h> 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 coordin
23、ate'); 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 X2zIFm %* _gfec4o % BEGIN TIME-STEPPING LOOP Z= LLL %* u
24、F ;8B" P_Pco for n=1:nmax rM4RibS 5Z(q|nn7P %* uG+eF % Update electric fields pf#R %* + jN)$Y3Ya x f)P ex(1:ie,2:je,2:ke)=ca*ex(1:ie,2:je,2:ke)+. >J,IxRGi cb*(hz(
25、1:ie,2:je,2:ke)-hz(1:ie,1:je-1,2:ke)+. Pk8(2fAYk hy(1:ie,2:je,1:ke-1)-hy(1:ie,2:je,2:ke); ()fYhk|W >?> !#1 ey(2:ie,1:je,2:ke)=ca*ey(2:ie,1:je,2:ke)+. C?rb(m &
26、#160; cb*(hx(2:ie,1:je,2:ke)-hx(2:ie,1:je,1:ke-1)+. 1 y7$"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)+. fM<g+X
27、 cb*(hx(2:ie,1:je-1,1:ke)-hx(2:ie,2:je,1:ke)+. r+n hm"9 hy(2:ie,2:je,1:ke)-hy(1:ie-1,2:je,1:ke); <h_7Dn rgu7g ez(is,js,1:ke)=ez(is,js,1
28、:ke)+. pJETM srcconst*(n-ndelay)*exp(-(n-ndelay)2/tau2); -PH qD j"<F?kQ %* V7>, % 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)+. ,:/3'
29、L db*(ey(2:ie,1:je,2:kb)-ey(2:ie,1:je,1:ke)+. .Ue1'v*, ez(2:ie,1:je,1:ke)-ez(2:ie,2:jb,1:ke); 2o-Ie/"d m_1BB$lyP2 hy(1:ie,2:je,
30、1:ke)=hy(1:ie,2:je,1:ke)+. AqPQeNgz db*(ex(1:ie,2:je,1:ke)-ex(1:ie,2:je,2:kb)+. u:D,;) ez(2:ib,2:je,1:ke)-ez(1:ie,2:je,1:ke); Sf*b6lcC WT>2
31、eMK hz(1:ie,1:je,2:ke)=hz(1:ie,1:je,2:ke)+. QWV12t$v db*(ex(1:ie,2:jb,2:ke)-ex(1:ie,1:je,2:ke)+. z/Yrf ey(1:ie,1:je,2:ke)-ey(2:ib,1:je,2:ke);
32、=%V(n7= F"Y.'my8 %* 6vQCghI % Visualize fields gK8=A0c %* A7qKY-4B HYf if mod(n,2)=0; $Dm2>:Dmt plRBfw>N timestep=int2str(n); BB694 tview(:,:)=ez(:,:,kobs); :d ts> sview(:,:)=ez(:,js,:); *+qlam4N >vPDF+u
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