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. We introduce some cheaper and faster variants of the classical additive Schwarz preconditioner (AS) for general sparse linear systems and show, by numerical examples, that the new methods are superior to AS in terms of both iteration counts and CPU time, as well as the communication cost when implemented on distributed memory computers. This is especially true for harder problems such as indefinite complex linear systems and systems of convection-di#usion equations from three-dimensional compressible flows. Both sequential and parallel results are reported. Key words. Overlapping domain decomposition, preconditioner, iterative method, sparse matrix AMS(MOS) subject classifications. 65N30, 65F10 1. Introduction. In this paper, we introduce some modified overlapping additive Schwarz preconditioners for sparse linear systems. The original additive Schwarz method (AS) was introduced for solving symmetric positive definite elliptic finite element problems, and was later extended to many...
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