Domain Decomposition with Nonmatching Grids for Exterior Transmission Problems via FEM and DtN Mapping

Abstract

In this paper, we are concerned with a non-overlapping domain decomposition method (DDM) for exterior transmission problems in the plane. Based on the natural boundary integral operator, we combine the DDM with a Dirichlet-to-Neumann (DtN) mapping and provide the numerical analysis with nonmatching grids. The weak continuity of the approximation solutions on the interface is imposed by a dual basis multiplier. We show that this multiplier space can generate optimal error estimate and obtain the corresponding rate of convergence. Finally, several numerical examples confirm the theoretical results.