Image:Helmholtz solution.png

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[edit] MATLAB source code

% Plot the solution to the Helmholtz equation with a given source
clear all;

Box_x = 3;
Scale = 0.5;
Box_y = Box_x/Scale;

Nx = 200;
Ny = Nx/Scale;

wavenumber = 10;

XX = linspace(-Box_x, Box_x, Nx);
YY = linspace(-Box_y, Box_y, Ny);
hx = XX(2) - XX(1);
hy = YY(2) - YY(1);
[X, Y] = meshgrid(XX, YY);

Source_size  = 0.5;
Source_shift = 2;
Source =  max(Source_size^2 - X.^2-(Y-Source_shift).^2, 0) + max(Source_size^2 - X.^2-(Y+Source_shift).^2, 0) ;

% plot the source
figure(1); clf; hold on; axis equal; axis off;
imagesc(Source);


% plot the solution to the Helmholtz equation
I = sqrt(-1);
Field = 0*X;

[m, n] = size(Source);
for i=1:m
   i
   for j=1:n

      if Source(i, j) ~= 0

         x0 = X(i, j);
         y0 = Y(i, j);

         % add the contribution from the current source
         Field = Field + (I/4)*besselh(0, 1, wavenumber*sqrt((X-x0).^2+(Y-y0).^2) + eps)*Source(i, j)*hx*hy;
      end
      
   end
end


figure(2); clf; hold on; axis equal; axis off;
imagesc(real(Field));

% Save to disk and convert to png right away
figure(1); 
saveas(gcf, 'Helmholtz_source.eps', 'psc2');
%! convert -density 200 Helmholtz_source.eps Helmholtz_source.png

figure(2); 
saveas(gcf, 'Helmholtz_solution.eps', 'psc2');
%! convert -density 200 Helmholtz_solution.eps Helmholtz_solution.png

• Helmholtz equation