Question

I have an FDTD assignment, it’s not going well. Whenever I put a source in and let the simulation run for a bit (Note – if you test you have to use the debugger and step through the loop increments otherwise there will be a hefty overflow).

In most of the simulations I’ve seen, people break Ex and Ey into separate parts, I put them into one large E matrix and used the index offset (seen in Ep(u,v+1) and E(u+1,v) to calculate Ey and Ex independently).

The sources I used for reference were:
http://fdtd.wikispaces.com/
and
http://www.mathworks.com/matlabcentral/fileexchange/21000-tiny-fdtd-v1-0
That one is acoustics, but works well.

    close all;


    %% Some user modifiable parameters
    mu0 = pi*4E-7; % pH/µm
    e0 =   8.854187E-12; % Picofarads/micron
    c = 1/sqrt(mu0*e0);

    cellsizeX = 100;      % Size of Yee-Cell in microns
    cellsizeY = 100;      % Size of Yee-Cell in microns
    numX = 100; % Number of cells in X direction
    numY = 100; % Number of cells in Y direction
    lambda = 700*10^-9;
    dx = lambda/20;
    dy = lambda/20;
    dt =  (c*sqrt(dx^-2+dy^-2))^-1;

    t0 = 100;       %index time of gaussian pulse peak
    width = 10;     %peakyness of gaussian pulse

    %% Initialise the H and E array
    H = zeros(2*numX, 2*numY);       
    Hp = zeros(2*numX, 2*numY);
    E = zeros(2*numX+1,2*numY+1);    
    Ep = zeros(2*numX+1,2*numY+1);    
    Etemp = zeros(2*numX+1,2*numY+1);
    Htemp = zeros(2*numX, 2*numY);
    P = zeros(2*numX+1,2*numY+1);
    Pp = zeros(2*numX+1,2*numY+1);

    % Scaling factors for H and E fields

    CEx = dt/(dx*mu0);
    CEy = dt/(dy*mu0);
    CHx = dt/(dy*e0);
    CHy = dt/(dx*e0);
    x = 2:2:2*numX; %2*numX-2;

    %Initialize Permibilities
    Perm = ones(2*numX+1,2*numY+1);


    %% FDTD loop
for n = 1:1500;

    if(n < 200)
        E(numX-10:2:numX+10,numY+1) =  1E-19*sin(2*pi*428E12*n*dt);    %exp(-.5 * ((n-t0)/width).^2); %insert hard source
    end;

    for u = 2:2:2*numX-1
        for v = 2:2:2*numY-1
            Hp(u,v) = H(u,v) + (dt/mu0)*( -(E(u+1,v) - E(u-1,v))/dx) + ( E(u,v+1) - E(u,v-1)/dy ); % Solving for Hplus
            Ep(u,v+1) = E(u,v+1) + (dt/(dy*e0))*(Hp(u,v+2) - Hp(u, v)); % Solving for Ex plus
            Ep(u+1, v) = E(u+1, v) - (dt/(dx*e0))*(Hp(u+2, v) - Hp(u, v)); % Solving for Ey plus

        end
    end;


    % Dirichlet Boundary Conditions
    Ep(1,:) = 0;
    Ep(:,1) = 0;
    Ep(2*numX+1,:) = 0;
    Ep(:,2*numX+1) = 0;

    % Plotting
    surf(Ep); shading interp; lighting phong; colormap hot; axis off; zlim([0 1]);
    set(gcf,'Color', [0 0 0], 'Number', 'on', 'Name', sprintf('FDTD Project, step = %i', n));
    %title(sprintf('Time = %.2f microsec',n*dt*1e12),'Color',[1 0 0],'FontSize', 22); 
    drawnow;

    E = Ep;
    H = Hp;



end;

end;

Answer 1

2 things:

1 – is Ep(:,2*numX+1,:) = 0; correct? (i.e. should it be Ep(:,2*numX+1) = 0;?)

2 – at the very end, I think you may want to change the code to

if (max(max(Ep)) > 1e-3)
      E = Ep/max(max(Ep));
else E = Ep;
end
if (max(max(Hp)) > 1e-3)
    H = Hp/max(max(Hp));
else H = Hp;
end

as max(Ep) will give you a 1×100 matrix. 1e-3 is for protection, you can lower it to whatever value you choose.