Hobby Projects

Periodically perforated domains

Diffusion in a domain with periodically distributed obstacles can be macroscopically approximated by a reduced diffusion constant. This so-called homogenized constant can be computed numerically by solving an associated partial differential equation in a single periodic cell (the so-called cell problem). The classical theory has been developed in this article.
I have implemented two different methods of computing the homogenized diffusion constant for obstacles of arbitrary shape. The figure shows the solution of the cell problem for a circular obstacle.

The source code is openly available at https://github.com/frank-roesler/PerfDoms