Solving Heat Diffusion / Finite difference problem, maybe on GPU?

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Raphaël 2018-8-8

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https://ww2.mathworks.cn/matlabcentral/answers/414047-solving-heat-diffusion-finite-difference-problem-maybe-on-gpu

Hi, I want to simulate a 3D heat diffusion problem with infinite border. At each time iteration there is other simulation running so it is going to be a code that will take time to run. Since the problem has a circular symmetry, I was able to simplify it to a 2D problem with one of the border being basically a mirror. Here's the equation:

dT/Dr * (dk/dr + k/r) + d^2(T)/dr^2 + dk/dz * dT/dz + k * d^2(T)/dz^2 + Q = rho*C*dT/dt

I know how to solve this problem with my own code but I was wondering if there was a simpler and faster way than writing my code. Is there something in matlab that has already been optimize to simulate that equation? On another note, is it possible (and is it worth it) to make the code run on my GPU instead of CPU to have it go faster. Remember at each time iteration I need to do several other computations.

Thank you for your advice.