The Use of Pointwise Interpolation in Domain Decomposition Methods with Nonnested Meshes

Abstract

In this paper, the author develops a new technique and a corresponding theory for Schwarz-type overlapping domain decomposition methods for solving large sparse linear systems which arise from finite element discretization of elliptic partial differential equations. The theory provides an optimal convergence of an additive Schwarz algorithm that is constructed with a nonnested coarse space and a not necessarily shape regular subdomain partitioning. The theory is also applicable to the graph partitioning algorithms recently developed by Cai and Saad [Overlapping domain decomposition algorithms for general sparse matrices, Preprint 93-027, Univ. of Minnesota] and Farhat and Lesoine [Internat. J. Numer. Methods Engrg., 36 (1993), pp. 745–764] for problems defined on unstructured meshes.