File:Helmholtz solution.png
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![File:Helmholtz solution.png](http://178.128.105.246/cars-https-upload.wikimedia.org/wikipedia/commons/thumb/3/34/Helmholtz_solution.png/298px-Helmholtz_solution.png?20070707195008)
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DescriptionHelmholtz solution.png | Illustration of en:Helmholtz equation. |
Date | (UTC) |
Source | self-made with en:Matlab. See the source code below. |
Author | Oleg Alexandrov |
![](http://178.128.105.246/cars-https-upload.wikimedia.org/wikipedia/commons/thumb/2/21/Matlab_Logo.png/25px-Matlab_Logo.png)
This diagram was created with MATLAB.
Public domainPublic domainfalsefalse |
![]() |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
% 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
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This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with
{{vector version available|new image name}} .
It is recommended to name the SVG file “Helmholtz solution.svg”—then the template Vector version available (or Vva) does not need the new image name parameter. |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 19:50, 7 July 2007 | ![]() | 975 × 1,957 (23 KB) | Oleg Alexandrov (talk | contribs) | Tweak |
04:18, 7 July 2007 | ![]() | 500 × 989 (22 KB) | Oleg Alexandrov (talk | contribs) | Higher res. | |
03:59, 7 July 2007 | ![]() | 500 × 989 (15 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=Illustration of en:Helmholtz equation. |Source=self-made with en:Matlab. See the source code below. |Date=03:56, 7 July 2007 (UTC) |Author= Oleg Alexandrov }} {{PD-self}} ==MATLAB source code |
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