Optimized Schwarz methods for unsymmetric layered problems with strongly discontinuous and anisotropic coefficients

In this paper we consider unsymmetric elliptic problems of advection–diffusion–reaction type, with strongly heterogeneous and anisotropic diffusion coefficients. We use non-overlapping Optimized Schwarz Methods (OSM) and we study new interface conditions where only one or two real parameters have to be chosen along the entire interface. Using one real parameter it is possible to design interface conditions of Robin type, whereas the use of two real parameters and of more general interface conditions allows to better take into account the heterogeneities of the medium. The analysis is made at the semi-discrete level, where the equation is discretized in the direction parallel to the interface, and kept continuous in the normal direction. Numerical results are given to validate the proposed interface conditions.