fdtd.m

FDTD code in Free Space with no absorbing boundary conditions.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FDTD  Finite-Difference Time-domain in free space no ABC 
% FDTD(t) runs FDTD for time t.
%
% FDTD implenments the FDTD/staggered leapfrog scheme
% over time 0-max_time and space 0-max_space.  This program
% simulates a gassian pulse in the grid specified with 
% max_time and max_space.  The pulse is sent from the center of
% the problem space and disperses in both directions
%-Kira Heater 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function FDTD = FDTD(time)



max_time = time;
max_space = 200;                    %must be divisible by two
eta = 1/2;

E = zeros(max_space,1);             %Initialize Electric array
H = E;                              %Initialize Magnetic array


spread = 12;                        %width of pulse
center_problem_space = max_space/2;
t0 = 40;                            %center of pulse


%Outer loop steps through time -
%here E is 1/2 step behind since the pulse
%enters the problem space between the 
%E and H loops.
for n = 1:max_time

    
    %Inner Loop E - Increments electric wave in space
    for k = 2:max_space
        E(k) =  E(k) + eta*( H(k-1)-H(k) );   
    end
    
  
    pulse = exp( -.5*( (t0-n)/spread )^2 ); %Hard Source- imposes a value on the grid
    E(center_problem_space) = pulse;
   
 
    %Inner Loop H - Increments magnetic wave in space
    for j = 1:max_space-1
        H(j) = H(j) + eta*( E(j)-E(j+1) );    
    end
     

     %Plots progression of the electric wave
       figure(1)
       plot(E)
       axis([1 max_space -1.1 1.1])
       title('FDTD Simulation of and Electric Pulse in Free Space')
       xlabel('Problem Space')
       ylabel('E_x')
       pause(.05)  
   
  end
   
    %Plots electric and magnetic feilds at max_time  
    figure(2)
    subplot(2,1,1)
    plot(E,'r')
    title('Simulation of Electric Pulse')
    ylabel('E_x')
    axis([0 max_space -1.1 1.1])
    subplot(2,1,2)
    plot(H,'g')
    ylabel('H_y')
    title('Simulation of Magnetic Pulse')
    axis([0 max_space -1.1 1.1])