an example MATLAB code for simulating a 2D FDTD problem

Here is an example MATLAB code for simulating a 2D FDTD problem:

% Define simulation parameters
dx = 0.01; % Spatial step size
dt = 0.0001; % Time step size
tmax = 1; % Maximum simulation time
L = 1; % Length of simulation domain
W = 1; % Width of simulation domain
x = 0:dx:L; % Spatial grid
y = 0:dx:W;
T = 0:dt:tmax; % Time grid
c = 1; % Wave speed

% Define source waveform
f0 = 1e9; % Center frequency of Gaussian pulse
t0 = 0.5e-9; % Width of Gaussian pulse
A = 1; % Amplitude of Gaussian pulse
source = A*exp(-((T-t0).^2)/(2*t0^2)).*sin(2*pi*f0*(T-t0));

% Initialize electric and magnetic fields
Ez = zeros(length(x),length(y),length(T));
Hy = zeros(length(x),length(y),length(T));

% Main FDTD loop
for n = 1:length(T)
    % Update magnetic field
    for i = 1:length(x)-1
        for j = 1:length(y)-1
            Hy(i,j,n+1) = Hy(i,j,n) + dt/(mu*dx)*(Ez(i,j+1,n) - Ez(i,j,n) - Ez(i+1,j,n) + Ez(i+1,j+1,n));
        end
    end
    % Update electric field
    for i = 2:length(x)-1
        for j = 2:length(y)-1
            Ez(i,j,n+1) = Ez(i,j,n) + dt/(eps*dx)*(Hy(i,j,n+1) - Hy(i,j-1,n+1) - Hy(i-1,j,n+1) + Hy(i-1,j-1,n+1));
        end
    end
    % Add source to electric field
    Ez(1,round(length(y)/2),n+1) = Ez(1,round(length(y)/2),n+1) + source(n);
end

% Plot results
figure;
for n = 1:length(T)
    surf(x,y,Ez(:,:,n)');
    shading interp;
    xlabel('x');
    ylabel('y');
    zlabel('Ez');
    title(['Time = ',num2str(T(n))]);
    axis([0 L 0 W -1 1]);
    pause(0.01);
end

This code simulates a 2D FDTD problem in a rectangular domain with a Gaussian pulse source at one edge. The electric and magnetic fields are updated using the FDTD method, and the results are plotted as a 3D surface over time.