/
Material3D.m
executable file
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Material3D.m
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%physical constants
clear all;
close all;
c = 2.998e8;
eta0 = 120*pi;
mu0 = pi*4e-7;
eps0 = 1e-9/(36*pi);
%box dimensions
width = 1;
height = 1;
length = 1;
%spatial discretization
dx = 0.02;
dy = dx;
dz = dx;
nx = width/dx;
ny = height/dy;
nz = length/dz;
%source
f0 =1e9;
tw = 1e-8/pi;
t0 = 4*tw;
srcx = round(nx / 2);
srcy = round(nz / 2);
srcz = round(3 * ny / 4);
%material
adipose = 10;
tumor = 60;
mx = 3 * ny / 8;
my = 0;
mz = 0;
mw = nx / 4; % width
mh = ny / 4; % height
ml = nz / 4; % length
al = ny / 2;
eps = ones(nx,ny,nz) * eps0;
for i=1:1:nx
for j=1:1:ny
for k=1:1:nz
% adipose tissue is located under z < al
if (k<al)
eps(i,j,k) = eps0 * adipose ;
end
if (i>mx && i<(mw+mx) && j>my && j<(mh+my) && k>mz && k<(ml+mz))
eps(i,j,k) = eps0 * tumor;
end
end
end
end
%temporal discretization
dt = 0.95/(c*sqrt(dx^-2+dy^-2+dz^-2));
n_iter = 5000;
%EM field dimensions
Hx = zeros(nx,ny,nz);
Hy = zeros(nx,ny,nz);
Hz = zeros(nx,ny,nz);
Ex = zeros(nx,ny,nz);
Ey = zeros(nx,ny,nz);
Ez = zeros(nx,ny,nz);
%iteration
i = 0;
for n=1:1:n_iter
%magnetic field derivatives
Hxy = diff(Hx,1,2);
Hxz = diff(Hx,1,3);
Hzx = diff(Hz,1,1);
Hzy = diff(Hz,1,2);
Hyx = diff(Hy,1,1);
Hyz = diff(Hy,1,3);
%electric field maxwell equations
Ex(:,2:end-1,2:end-1) = Ex(:,2:end-1,2:nz-1) + (dt/(eps(:,2:end-1,2:nz-1)*dy)).*Hzy(:,1:end-1,2:end-1) - (dt/(eps(:,2:end-1,2:nz-1)*dz)).*Hyz(:,2:ny-1,1:end-1);
Ey(2:end-1,:,2:end-1) = Ey(2:end-1,:,2:end-1) + (dt/(eps(2:end-1,:,2:end-1)*dz)).*Hxz(2:end-1,:,1:end-1) - (dt/(eps(2:end-1,:,2:end-1)*dx)).*Hzx(1:end-1,:,2:end-1);
Ez(2:end-1,2:end-1,:) = Ez(2:end-1,2:end-1,:) + (dt/(eps(2:end-1,2:end-1,:)*dx)).*Hyx(1:end-1,2:end-1,:) - (dt/(eps(2:end-1,2:end-1,:)*dy)).*Hxy(2:end-1,1:end-1,:);
%gaussian source
f = sin(2*pi*f0*n*dt)*exp(-(n*dt-t0)^2/(tw^2))/dy;
Ez(srcx,srcy,srcz) = Ez(srcx,srcy,srcz) + f;
%Ezn(n)=Ez(srcx,srcy,srcz);
%electric field derivatives
Exy = diff(Ex,1,2);
Exz = diff(Ex,1,3);
Ezx = diff(Ez,1,1);
Ezy = diff(Ez,1,2);
Eyx = diff(Ey,1,1);
Eyz = diff(Ey,1,3);
%magnetic field maxwell equations
Hx(:,1:end-1,1:end-1) = Hx(:,1:end-1,1:end-1) - (dt/(mu0*dy))*Ezy(:,:,1:end-1) + (dt/(mu0*dz))*Eyz(:,1:end-1,:);
Hy(1:end-1,:,1:end-1) = Hy(1:end-1,:,1:end-1) - (dt/(mu0*dz))*Exz(1:end-1,:,:) + (dt/(mu0*dx))*Ezx(:,:,1:end-1);
Hz(1:end-1,1:end-1,:) = Hz(1:end-1,1:end-1,:) - (dt/(mu0*dx))*Eyx(:,1:end-1,:) + (dt/(mu0*dy))*Exy(1:end-1,:,:);
%display
if (mod(i,10)==0)
slice(:,:)=Ez(nx/2,:,:);
pcolor(slice);
colorbar;
drawnow
end
i = i+1
end