Domain decomposition preconditioner for anisotropic diffusion

Abstract

We propose and investigate two-level preconditioners for the diffusion equations with anisotropic coefficients in model polyhedral domains. Preconditioners are based on a partitioning of the mesh in (x, y)-plane into non-overlapping subdomains and on a special coarsening algorithm in each of the mesh layers. The condition number of the preconditioned matrix does not depend on the coefficients in the diffusion operator. Numerical experiments confirm the theoretical results.