Hi there. I am writing a code to solve the diffusion equation in two dimensions using the Alternate Directions Implicit method: https://en.wikipedia.org/wiki/Alternating_direction_implicit_method(adsbygoogle = window.adsbygoogle || []).push({});

I haven't finished to write the code yet, but I am trying to be the most general as possible. However, in the bibliography I have found almost exclusively the case for homogeneous media, and the stability analysis is done for that case, in which the matrices to be inverted are symmetric. I know that going to 3D is complicated because the Peaceman-Rachford scheme isn't stable. However, I wanted to know if there is any analysis reported in the bibliography for the inhomogeneous media case. I will finish to write the code and experiment with it by my self, but I was trying to avoid the analytical part. I have already written the algorithm, so I'm just coding right now.

I also would like to pose the question on why the homogeneous case is so widely reported, when the inhomogeneous is much more general and useful I think. Is there any numerical trick to use the homogeneous media solution to solve the inomogeneous media case in an efficient way? perhaps recursively, using finite differences?

Thanks in advance.

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# A Some questions regarding the ADI Method

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