MATLAB, 3d finite difference method for heat equation

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MATLAB >> 3d finite difference method for heat equation

by Tobias Schmid » Wed, 29 Oct 2003 17:52:15 GMT

Hi guys


Did somebody of You guys write already a finite difference scheme for
the 3d heat equation. I know how to write it by myself, but I'm kind
of in
a hurry, and would like to concentrate on the main problems. If
somebody
of You guys wrote already a small program for a 3d finite difference
scheme
please let me know.


Have a good one.


Tobi
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MATLAB >> 3d finite difference method for heat equation

by ayuda » Thu, 30 Oct 2003 06:14:48 GMT



Since you can write a code for solving a 3D heat equation by yourself, it
will be a good idea to try. But if your are so busy and concentrated in the
main problems :) here is one solution:

Let "u" be your initial 3D data, "dt" the time step, and "maxit" the number
of iterations. Then a solution to 3D heat equation
" u_t = \Delta u " with a predefined initial condition "u_0" would be:
==========================================
dt = 1/6; maxit = 50;
[m,n,p] = size(u);
% Initialize result
v = u;
for i = 1:maxit
vxx = (v([2:m m],[1:n],[1:p]) + v([1 1:m-1],[1:n],[1:p]) -...
2.*v([1:m],[1:n],[1:p]))./4;
vyy = (v([1:m],[2:n n],[1:p]) + v([1:m],[1 1:n-1],[1:p]) -...
2.*v([1:m],[1:n],[1:p]))./4;
vzz = (v([1:m],[1:n],[2:p p]) + v([1:m],[1:n],[1 1:p-1]) -...
2.*v([1:m],[1:n],[1:p]))./4;
% Discretization of Laplacian: Deltav = v_xx + v_yy + v_zz
Deltav = vxx + vyy + vzz;
% Update result
v = v + dt*Deltav;
end;
==========================================

Ayuda.
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MATLAB >> 3d finite difference method for heat equation

by MZ Zahoor » Thu, 23 Dec 2010 02:26:20 GMT

Hi Ayuda,

I tried your solution to different mesh sizes. The results come out to be different, which means there is no convergence. DO you think your matlab solution is 100% correct?

Thanks,

~ MZ
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