A domain decomposition preconditioner of neumann-neumann type for the stokes equations

Vitorita Dolean, Frédéric Nataf, Gerd Rapin

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Abstract

In this paper we recall a new domain decomposition method for the Stokes problem obtained via the Smith factorization. From the theoretical point of view, this domain decomposition method is optimal in the sense that it converges in two iterations for a decomposition into two equal domains. Previous results illustrated the fast convergence of the proposed algorithm in some cases. Our algorithm has shown a more robust behavior than Neumann-Neumann or FETI type methods for particular decompositions; as far as general decompositions are concerned, the performances of the three algorithms are similar. Nevertheless, the computations of the singular values of the interface preconditioned problem have shown that one needs a coarse space whose dimension is less than the one needed for the Neumann-Neumann algorithm. In this work we present a new strategy in order to improve the convergence of the new algorithm in the presence of cross points.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XVIII
PublisherSpringer
Pages161-168
Number of pages8
Volume70
ISBN (Print)9783642026768
DOIs
Publication statusPublished - 12 Oct 2009
Event18th International Conference of Domain Decomposition Methods - Jerusalem, Israel
Duration: 12 Jan 200817 Jan 2008

Publication series

NameLecture Notes in Computational Science and Engineering
Volume70 LNCSE
ISSN (Print)1439-7358

Conference

Conference18th International Conference of Domain Decomposition Methods
CountryIsrael
CityJerusalem
Period12/01/0817/01/08

Keywords

  • domain decomposition methods
  • algorithms
  • convergence of numerical methods
  • decomposition
  • operations research
  • cross point
  • fast convergence
  • preconditioners
  • Stokes equations

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