THE USE OF POINTWISE INTERPOLATION IN DOMAIN DECOMPOSITION METHODS WITH NONNESTED MESHES

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 di scretization of elliptic partial differential equations. The theory pr ovides 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 [Over lapping domain decomposition algorithms for general sparse matrices, P reprint 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.