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Abstract : |
Abstract. The classical Schwarz alternating method has recently been generalized in several directions. This effort has resulted in a number of new powerful domain decomposition methods for elliptic problems, in new insight into multigrid methods and in the development of a very useful framework for the analysis of a variety of iterative methods. Most of this work has focused on positive definite, symmetric problems. In this paper a general framework is developed for multiplicative Schwarz algorithms for nonsymmetric and indefinite problems. Several applications are then discussed including two- and multi-level Schwarz methods and iterative substructuring algorithms. Some new results on additive Schwarz methods are also presented. Key words. nonsymmetric elliptic problems, preconditioned conjugate gradient type methods, finite elements, multiplicative Schwarz algorithms, |
