Improved ad hoc interface conditions for Schwarz solution procedure tuned to highly heterogeneous media

In this paper, an improved method to derive efficient interface conditions for the Schwarz solution procedure tuned to highly heterogeneous media is presented. This method, based on two parameters optimization, involves new interface conditions specially designed to keep the heterogeneity between the subdomains on the interface. The mathematical analysis of these interface conditions is first presented. Then the asymptotic analysis upon the mesh size parameter together with the heterogeneity ratio is detailed. These interface conditions lead to better asymptotic convergence rate than other available interface conditions. Numerical experiments illustrate the dependence of the proposed method upon several parameters, and confirm the robustness and efficiency of the Schwarz algorithm when equipped with such interface conditions.