%*********************************************************************** 
%    3-D FDTD code with PEC boundaries 
%*********************************************************************** 
% 
%    Program author: Susan C. Hagness 
%                    Department of Electrical and Computer Engineering 
%                    University of Wisconsin-Madison 
%                    1415 Engineering Drive 
%                    Madison, WI 53706-1691 
%                    608-265-5739 
%                    hagness@engr.wisc.edu 
% 
%    Date of this version:  February 2000 
% 
%    This MATLAB M-file implements the finite-difference time-domain 
%    solution of Maxwell's curl equations over a three-dimensional 
%    Cartesian space lattice comprised of uniform cubic grid cells. 
% 
%    To illustrate the algorithm, an air-filled rectangular cavity 
%    resonator is modeled.  The length, width, and height of the 
%    cavity are 10.0 cm (x-direction), 4.8 cm (y-direction), and 
%    2.0 cm (z-direction), respectively. 
% 
%    The computational domain is truncated using PEC boundary 
%    conditions: 
%          ex(i,j,k)=0 on the j=1, j=jb, k=1, and k=kb planes 
%          ey(i,j,k)=0 on the i=1, i=ib, k=1, and k=kb planes 
%          ez(i,j,k)=0 on the i=1, i=ib, j=1, and j=jb planes 
%    These PEC boundaries form the outer lossless walls of the cavity. 
% 
%    The cavity is excited by an additive current source oriented 
%    along the z-direction.  The source waveform is a differentiated 
%    Gaussian pulse given by 
%          J(t)=-J0*(t-t0)*exp(-(t-t0)^2/tau^2), 
%    where tau=50 ps.  The FWHM spectral bandwidth of this zero-dc- 
%    content pulse is approximately 7 GHz. The grid resolution 
%    (dx = 2 mm) was chosen to provide at least 10 samples per 
%    wavelength up through 15 GHz. 
% 
%    To execute this M-file, type "fdtd3D" at the MATLAB prompt. 
%    This M-file displays the FDTD-computed Ez fields at every other 
%    time step, and records those frames in a movie matrix, M, which 
%    is played at the end of the simulation using the "movie" command. 
% 
%*********************************************************************** 

clear 

%*********************************************************************** 
%    Fundamental constants 
%*********************************************************************** 

cc=2.99792458e8;            %speed of light in free space 
muz=4.0*pi*1.0e-7;          %permeability of free space 
epsz=1.0/(cc*cc*muz);      %permittivity of free space 

%*********************************************************************** 
%    Grid parameters 
%*********************************************************************** 

ie=50;      %number of grid cells in x-direction 
je=24;      %number of grid cells in y-direction 
ke=10;      %number of grid cells in z-direction 

ib=ie+1; 
jb=je+1; 
kb=ke+1; 

is=26;      %location of z-directed current source 
js=13;      %location of z-directed current source 

kobs=5; 

dx=0.002;          %space increment of cubic lattice 
dt=dx/(2.0*cc);    %time step 

nmax=500;          %total number of time steps 


%*********************************************************************** 
%    Differentiated Gaussian pulse excitation 
%*********************************************************************** 

rtau=50.0e-12; 
tau=rtau/dt; 
ndelay=3*tau; 
srcconst=-dt*3.0e+11; 

%*********************************************************************** 
%    Material parameters 
%*********************************************************************** 

eps=1.0; 
sig=0.0; 

%*********************************************************************** 
%    Updating coefficients 
%*********************************************************************** 

ca=(1.0-(dt*sig)/(2.0*epsz*eps))/(1.0+(dt*sig)/(2.0*epsz*eps)); 
cb=(dt/epsz/eps/dx)/(1.0+(dt*sig)/(2.0*epsz*eps)); 
da=1.0; 
db=dt/muz/dx; 

%*********************************************************************** 
%    Field arrays 
%*********************************************************************** 

ex=zeros(ie,jb,kb); 
ey=zeros(ib,je,kb); 
ez=zeros(ib,jb,ke); 
hx=zeros(ib,je,ke); 
hy=zeros(ie,jb,ke); 
hz=zeros(ie,je,kb); 

%*********************************************************************** 
%    Movie initialization 
%*********************************************************************** 

tview(:,:)=ez(:,:,kobs); 
sview(:,:)=ez(:,js,:); 

subplot('position',[0.15 0.45 0.7 0.45]),pcolor(tview'); 
shading flat; 
caxis([-1.0 1.0]); 
colorbar; 
axis image; 
title(['Ez(i,j,k=5), time step = 0']); 
xlabel('i coordinate'); 
ylabel('j coordinate'); 

subplot('position',[0.15 0.10 0.7 0.25]),pcolor(sview'); 
shading flat; 
caxis([-1.0 1.0]); 
colorbar; 
axis image; 
title(['Ez(i,j=13,k), time step = 0']); 
xlabel('i coordinate'); 
ylabel('k coordinate'); 

rect=get(gcf,'Position'); 
rect(1:2)=[0 0]; 

M=moviein(nmax/2,gcf,rect); 

%*********************************************************************** 
%    BEGIN TIME-STEPPING LOOP 
%*********************************************************************** 

for n=1:nmax 

%*********************************************************************** 
%    Update electric fields 
%*********************************************************************** 

ex(1:ie,2:je,2:ke)=ca*ex(1:ie,2:je,2:ke)+... 
                  cb*(hz(1:ie,2:je,2:ke)-hz(1:ie,1:je-1,2:ke)+... 
                      hy(1:ie,2:je,1:ke-1)-hy(1:ie,2:je,2:ke)); 

ey(2:ie,1:je,2:ke)=ca*ey(2:ie,1:je,2:ke)+... 
                  cb*(hx(2:ie,1:je,2:ke)-hx(2:ie,1:je,1:ke-1)+... 
                      hz(1:ie-1,1:je,2:ke)-hz(2:ie,1:je,2:ke)); 

ez(2:ie,2:je,1:ke)=ca*ez(2:ie,2:je,1:ke)+... 
                  cb*(hx(2:ie,1:je-1,1:ke)-hx(2:ie,2:je,1:ke)+... 
                      hy(2:ie,2:je,1:ke)-hy(1:ie-1,2:je,1:ke)); 

ez(is,js,1:ke)=ez(is,js,1:ke)+... 
              srcconst*(n-ndelay)*exp(-((n-ndelay)^2/tau^2)); 

%*********************************************************************** 
%    Update magnetic fields 
%*********************************************************************** 

hx(2:ie,1:je,1:ke)=hx(2:ie,1:je,1:ke)+... 
                  db*(ey(2:ie,1:je,2:kb)-ey(2:ie,1:je,1:ke)+... 
                      ez(2:ie,1:je,1:ke)-ez(2:ie,2:jb,1:ke)); 

hy(1:ie,2:je,1:ke)=hy(1:ie,2:je,1:ke)+... 
                  db*(ex(1:ie,2:je,1:ke)-ex(1:ie,2:je,2:kb)+... 
                      ez(2:ib,2:je,1:ke)-ez(1:ie,2:je,1:ke)); 

hz(1:ie,1:je,2:ke)=hz(1:ie,1:je,2:ke)+... 
                  db*(ex(1:ie,2:jb,2:ke)-ex(1:ie,1:je,2:ke)+... 
                      ey(1:ie,1:je,2:ke)-ey(2:ib,1:je,2:ke)); 

%*********************************************************************** 
%    Visualize fields 
%*********************************************************************** 

if mod(n,2)==0; 

timestep=int2str(n); 
tview(:,:)=ez(:,:,kobs); 
sview(:,:)=ez(:,js,:); 

subplot('position',[0.15 0.45 0.7 0.45]),pcolor(tview'); 
shading flat; 
caxis([-1.0 1.0]); 
colorbar; 
axis image; 
title(['Ez(i,j,k=5), time step = ',timestep]); 
xlabel('i coordinate'); 
ylabel('j coordinate'); 

subplot('position',[0.15 0.10 0.7 0.25]),pcolor(sview'); 
shading flat; 
caxis([-1.0 1.0]); 
colorbar; 
axis image; 
title(['Ez(i,j=13,k), time step = ',timestep]); 
xlabel('i coordinate'); 
ylabel('k coordinate'); 

nn=n/2; 
M(:,nn)=getframe(gcf,rect); 

end; 

%*********************************************************************** 
%    END TIME-STEPPING LOOP 
%*********************************************************************** 

end 

movie(gcf,M,0,10,rect);