Abstract

. In this paper, we develop 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 non-nested coarse space, and a not necessarily shape regular subdomain partitioning. The theory is also applicable to the graph partitioning algorithms recently developed, [5, 15], for problems defined on unstructured meshes. Key words. unstructured grids, non-nested meshes, domain decomposition, iterative method. AMS(MOS) subject classifications. 65F10, 65N30. 1. Introduction. Considerable interest has developed in Schwarz type overlapping domain decomposition methods for the numerical solution of partial differential equations; see for examples [2, 3, 4, 6, 7, 12, 13, 18] and the references therein. This class of methods o...

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