Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces

In this paper, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. We suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.