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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Some questions regarding the ADI Method

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**