Studies in Domain Decomposition: Multilevel Methods and the Biharmonic Dirichlet Problem (Classic Reprint) - Hardcover

Zhang, Xuejun

9780266272953: Studies in Domain Decomposition: Multilevel Methods and the Biharmonic Dirichlet Problem (Classic Reprint)

Hardcover

ISBN 10: 0266272959 ISBN 13: 9780266272953

Publisher: Forgotten Books, 2019

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Excerpt from Studies in Domain Decomposition: Multilevel Methods and the Biharmonic Dirichlet Problem

Multilevel methods, such as multigrid methods, are among the most efficient methods for linear equations arising from elliptic problems; cf. Hackbusch mccormick [38] and the references therein. Recently, with the increasing interest in parallel computation, several new multilevel methods have been developed; cf. Yserentant Bank, Dupont and Yserentant Bramble, Pasciak and Xu and Dryja and Widlund In this thesis, we give improved results for a class of multilevel methods by showing that the condition number of the iteration Operator grows at most linearly with the number of levels in general, and is bounded by a constant independent of the mesh sizes and the number of levels if the elliptic problem is Hz - regular. This is an improvement on Dryja and Widlund's results on a multilevel additive Schwarz method as well as Bramble, P-asciak and Ku's results on the bpx algorithm.

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