?? 2d-fdtd.m
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function FDTD_2D_Yee_2D_TM_final
%constants
c_0 = 3E8; % Speed of light in free space
mu_0 = 4.0*pi*1.0e-7; % Permeability of free space
eps_0 = 1.0/(c_0*c_0*mu_0); % Permittivty of free space
%to be set
Nx = 100; % Number of cells in x-direction
Ny = 100; % Number of cells in y-direction
Nt = 500; % Number of time steps
c_ref = c_0; % Reference velocity
eps_ref = eps_0;
mu_ref = mu_0;
f_0 = 10e9; % Excitation frequency
f_ref = f_0; % Reference frequency
omega_0 = 2.0*pi*f_0; % Excitation circular frequency
omega_ref = omega_0;
lambda_ref = c_ref/f_ref; % Reference wavelength
Dx_ref = lambda_ref/20; % Reference cells width
Dy_ref = lambda_ref/20;
X = Nx*Dx_ref;
Y = Ny*Dy_ref;
r = 0.5; % Normalized factor
Dt_ref = r/c_ref*Dx_ref; % Reference time step
Dt = Dt_ref;
% initialization
Ez0 = zeros(Nx, Ny);
Ez1 = zeros(Nx, Ny);
Hx0 = zeros(Nx, Ny);
Hx1 = zeros(Nx, Ny);
Hy0 = zeros(Nx, Ny);
Hy1 = zeros(Nx, Ny);
% Source position
Nx_Source = int16(0.5*(Nx+1));
Ny_Source = int16(0.5*(Nx+1));
pulse = 0;
for n = 1:Nt % Sources' definitions
t = Dt_ref*r*n; % Actual time
Source_type = 1; % Choice of source type
switch Source_type
case 1 % Modified source function
ncycles = 1;
if t < ncycles*2.0*pi/(omega_0)
pulse = -0.5*( 1.0 - cos(omega_0*t/ncycles) ) * sin(omega_0*t);
else
pulse = 0;
end
case 2 % Sigle cos source function
if t < 2.0*pi/(omega_0)
pulse = 8*c_0^2*Dt_ref^2*mu_ref*omega_0*cos(omega_0*t);
else
pulse = 0;
end
case 3 % Gaussian pulse
if t < Dt_ref*r*50
pulse = -40*c_0*(t-t*25/(n-1))*exp(-(t-t*25/(n-1))^2/2/(50/2.3548)^2/(t/(n-1))^2);
else
pulse = 0;
end
otherwise % For debug
pulse = 1;
end
Ez0(Nx_Source,Ny_Source) = Ez0(Nx_Source,Ny_Source) - r*pulse;
CHy = Dt_ref/mu_ref/Dx_ref; % Coefficients used below
CHx = Dt_ref/mu_ref/Dy_ref;
CEzHy = Dt_ref/eps_ref/Dx_ref;
CEzHx = Dt_ref/eps_ref/Dy_ref;
for i = 2:Nx
% H update
Hx1(i,1:Ny-1) = Hx0(i,1:Ny-1) - CHx.*(Ez0(i,2:Ny)-Ez0(i,1:Ny-1));
end
for i = 1:Nx-1
Hy1(i,2:Ny) = Hy0(i,2:Ny) + CHy.*(Ez0(i+1,2:Ny)-Ez0(i,2:Ny));
end
% Boundary conditions **************************************
boundary = 3; % Choice: '1'=Mur ABC; '2'=Dirichlet; '3'=Neumann
switch boundary
case 1 % For H Mur ABC
Hx1(1,1:Ny-1) = Hx0(2, 1:Ny-1) + (r-1)/(r+1).*(Hx1(2, 1:Ny-1)-Hx0(1,1:Ny-1)); % Mur ABC @ left side x = 0
Hx1(1:Nx, Ny) = Hx0(1:Nx,Ny-1) + (r-1)/(r+1).*(Hx1(1:Nx,Ny-1)-Hx0(1:Nx, Ny)); % Mur ABC @ left side y = Ny
Hy1(1:Nx-1,1) = Hy0(1:Nx-1, 2) + (r-1)/(r+1).*(Hy1(1:Nx-1, 2)-Hy0(1:Nx-1,1)); % Mur ABC @ left side y = 0
Hy1(Nx, 1:Ny) = Hy0(Nx-1,1:Ny) + (r-1)/(r+1).*(Hy1(Nx-1,1:Ny)-Hy0(Nx, 1:Ny)); % Mur ABC @ left side x = Nx
case 2 % Dirichlet
Hx1(1:Nx, 1) = 0;
Hx1(1:Nx,Ny) = 0;
Hx1(1, 1:Ny) = 0;
Hx1(Nx,1:Ny) = 0;
Hy1(1:Nx, 1) = 0;
Hy1(1:Nx,Ny) = 0;
Hy1(1, 1:Ny) = 0;
Hy1(Nx,1:Ny) = 0;
case 3 % Neumann
Hx1(1, 1:Ny-1) = Hx0(1, 1:Ny-1);
Hx1(Nx,1:Ny-1) = Hx1(Nx,1:Ny-1);
Hx1(1:Nx, Ny) = Hx0(1:Nx, Ny);
Hx1(1:Nx, 1) = Hx1(1:Nx, 1);
Hy1(1:Nx-1, 1) = Hy0(1:Nx-1, 1);
Hy1(1:Nx-1,Ny) = Hy0(1:Nx-1,Ny);
Hy1(Nx, 1:Ny) = Hy0(Nx, 1:Ny);
Hy1(1, 1:Ny) = Hy0(1, 1:Ny);
end
for i = 2:Nx
% E update
Ez1(i,2:Ny) = Ez0(i,2:Ny) + CEzHy.*(Hy1(i,2:Ny)-Hy1(i-1,2:Ny)) - CEzHx.*(Hx1(i,2:Ny)-Hx1(i,1:Ny-1));
end
switch boundary
case 1 % For E Mur ABC
Ez1(1,1:Ny) = Ez0(2,1:Ny) + (r-1)/(r+1).*(Ez1(2,1:Ny)-Ez0(1,1:Ny)); % Mur ABC @ right side x = 0
Ez1(1:Nx,1) = Ez0(1:Nx,2) + (r-1)/(r+1).*(Ez1(1:Nx,2)-Ez0(1:Nx,1)); % Mur ABC @ right side y = 0
case 2 % Dirichlet
Ez1(1, 1:Ny) = 0;
Ez1(1:Nx, 1) = 0;
Ez1(Nx,1:Ny) = 0;
Ez1(1:Nx,Ny) = 0;
case 3 % Neumann
Ez1(1, 1:Ny) = Ez0(1, 1:Ny);
Ez1(Nx,1:Ny) = Ez0(Nx,1:Ny);
Ez1(1:Nx, 1) = Ez0(1:Nx, 1);
Ez1(1:Nx,Ny) = Ez0(1:Nx,Ny);
end
Hx0 = Hx1;
Hy0 = Hy1;
Ez0 = Ez1;
% Display*********************************************
i = 1:Nx;
j = 1:Ny;
display = 1; % Choice: '1' = Ez, '2' = Hx, '3' = Hy, 'Otherwise' = three components
switch display
case 1
surf(i,j,Ez0);
axis([0 Nx 0 Ny -0.03 0.03]);
set(gca, 'XTick',[1 Nx/4 Nx/2 3*Nx/4 Nx],'FontSize',8);
set(gca, 'XTickLabel',[0 X/4 X/2 3*X/4 X],'FontSize',8);
xlabel('x in m');
set(gca, 'YTick',[1 Ny/4 Ny/2 3*Ny/4 Ny],'FontSize',8);
set(gca, 'YTickLabel',[0 Y/4 Y/2 3*Y/4 Y],'FontSize',8);
ylabel('y in m');
zlabel('Amplitude of Ez');
case 2
surf(i,j,Hx0);
axis([0 Nx 0 Ny -1e-4 1e-4]);
set(gca, 'XTick',[1 Nx/4 Nx/2 3*Nx/4 Nx],'FontSize',8);
set(gca, 'XTickLabel',[0 X/4 X/2 3*X/4 X],'FontSize',8);
xlabel('x in m');
set(gca, 'YTick',[1 Ny/4 Ny/2 3*Ny/4 Ny],'FontSize',8);
set(gca, 'YTickLabel',[0 Y/4 Y/2 3*Y/4 Y],'FontSize',8);
ylabel('y in m');
zlabel('Amplitude of Hx');
case 3
surf(i,j,Hy0);
axis([0 Nx 0 Ny -1e-4 1e-4]);
set(gca, 'XTick',[1 Nx/4 Nx/2 3*Nx/4 Nx],'FontSize',8);
set(gca, 'XTickLabel',[0 X/4 X/2 3*X/4 X],'FontSize',8);
xlabel('x in m');
set(gca, 'YTick',[1 Ny/4 Ny/2 3*Ny/4 Ny],'FontSize',8);
set(gca, 'YTickLabel',[0 Y/4 Y/2 3*Y/4 Y],'FontSize',8);
ylabel('y in m');
zlabel('Amplitude of Hy');
otherwise
subplot(2,2,1);
surf(i,j,Ez0);
title('Ex');
axis([0 Nx 0 Ny -0.03 0.03]);
set(gca, 'XTick',[1 Nx/4 Nx/2 3*Nx/4 Nx],'FontSize',8);
set(gca, 'XTickLabel',[0 X/4 X/2 3*X/4 X],'FontSize',8);
xlabel('x in m');
set(gca, 'YTick',[1 Ny/4 Ny/2 3*Ny/4 Ny],'FontSize',8);
set(gca, 'YTickLabel',[0 Y/4 Y/2 3*Y/4 Y],'FontSize',8);
ylabel('y in m');
zlabel('Amplitude of Ez');
subplot(2,2,2);
surf(i,j,Hx0);
title('Hx');
axis([0 Nx 0 Ny -1e-4 1e-4]);
set(gca, 'XTick',[1 Nx/4 Nx/2 3*Nx/4 Nx],'FontSize',8);
set(gca, 'XTickLabel',[0 X/4 X/2 3*X/4 X],'FontSize',8);
xlabel('x in m');
set(gca, 'YTick',[1 Ny/4 Ny/2 3*Ny/4 Ny],'FontSize',8);
set(gca, 'YTickLabel',[0 Y/4 Y/2 3*Y/4 Y],'FontSize',8);
ylabel('y in m');
zlabel('Amplitude of Hx');
subplot(2,2,3);
surf(i,j,Hy0);
title('Hy');
axis([0 Nx 0 Ny -1e-4 1e-4]);
set(gca, 'XTick',[1 Nx/4 Nx/2 3*Nx/4 Nx],'FontSize',8);
set(gca, 'XTickLabel',[0 X/4 X/2 3*X/4 X],'FontSize',8);
xlabel('x in m');
set(gca, 'YTick',[1 Ny/4 Ny/2 3*Ny/4 Ny],'FontSize',8);
set(gca, 'YTickLabel',[0 Y/4 Y/2 3*Y/4 Y],'FontSize',8);
ylabel('y in m');
zlabel('Amplitude of Hy');
end
%surf(i,j,Ez0);
%axis([0 Nx 0 Ny -0.03 0.03])
%A = rot90(Ez0);
%imagesc(A);
pause(0.005);
end
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