Heterogeneous domain decomposition method for high contrast dense composites

This paper is on numerical treatment of problems that describe high contrast composite materials with complex geometry. In particular, a heterogeneous domain decomposition method for a class of diffusion problems with rapidly oscillating coefficients that also have large variation of values within the domain is proposed. The method combines a FEM discretization in one subdomain with an asymptotic representation of the Dirichlet to Neumann map for the other subdomain. Numerical results that demonstrate the feasibility of the proposed approach are also provided.