Domain Decomposition with Nonmatching Grids for Exterior Transmission Problems via FEM and DtN Mapping (Journal of Computational Mathematics, 2006)
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.
Keywords: Domain decomposition; Nature boundary element; Nonmatching grids; Weak continuity; D-N alternating; Dual basis; Projection operator; Error estimate.