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

Vitorita Dolean, Frédéric Nataf, Gerd Rapin

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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

Fingerprint

Stokes Equations
Domain Decomposition
Preconditioner
Decomposition
Domain decomposition methods
Domain Decomposition Method
Decompose
Stokes Problem
Singular Values
Factorization
Converge
Iteration

Keywords

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

Cite this

Dolean, V., Nataf, F., & Rapin, G. (2009). A domain decomposition preconditioner of neumann-neumann type for the stokes equations. In Domain Decomposition Methods in Science and Engineering XVIII (Vol. 70, pp. 161-168). (Lecture Notes in Computational Science and Engineering; Vol. 70 LNCSE). Springer. https://doi.org/10.1007/978-3-642-02677-5_16
Dolean, Vitorita ; Nataf, Frédéric ; Rapin, Gerd. / A domain decomposition preconditioner of neumann-neumann type for the stokes equations. Domain Decomposition Methods in Science and Engineering XVIII. Vol. 70 Springer, 2009. pp. 161-168 (Lecture Notes in Computational Science and Engineering).
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Dolean, V, Nataf, F & Rapin, G 2009, A domain decomposition preconditioner of neumann-neumann type for the stokes equations. in Domain Decomposition Methods in Science and Engineering XVIII. vol. 70, Lecture Notes in Computational Science and Engineering, vol. 70 LNCSE, Springer, pp. 161-168, 18th International Conference of Domain Decomposition Methods, Jerusalem, Israel, 12/01/08. https://doi.org/10.1007/978-3-642-02677-5_16

A domain decomposition preconditioner of neumann-neumann type for the stokes equations. / Dolean, Vitorita; Nataf, Frédéric; Rapin, Gerd.

Domain Decomposition Methods in Science and Engineering XVIII. Vol. 70 Springer, 2009. p. 161-168 (Lecture Notes in Computational Science and Engineering; Vol. 70 LNCSE).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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Dolean V, Nataf F, Rapin G. A domain decomposition preconditioner of neumann-neumann type for the stokes equations. In Domain Decomposition Methods in Science and Engineering XVIII. Vol. 70. Springer. 2009. p. 161-168. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-642-02677-5_16