How to use the smith factorization for domain decomposition methods applied to the stokes equations

Victorita Dolean, Frédéric Nataf, Gerd Rapin

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

2 Citations (Scopus)
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Abstract

In this paper we demonstrate that the Smith factorization is a powerful tool to derive new domain decomposition methods for vector valued problems. Here, the factorization is applied to the two-dimensional Stokes system. The key idea is the transformation of the Stokes problem into a scalar bi-harmonic problem. We show how a proposed domain decomposition method for the bi-harmonic problem leads to an algorithm for the Stokes equations which inherits the convergence behavior of the scalar problem.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XVII
PublisherSpringer
Pages477-484
Number of pages8
Volume60
ISBN (Print)9783540751984
DOIs
Publication statusPublished - 1 Dec 2008
Event17th International Conference on Domain Decomposition Methods - St. Wolfgang /Strobl, Austria
Duration: 3 Jul 20067 Jul 2006

Publication series

NameLecture Notes in Computational Science and Engineering
Volume60
ISSN (Print)1439-7358

Conference

Conference17th International Conference on Domain Decomposition Methods
CountryAustria
CitySt. Wolfgang /Strobl
Period3/07/067/07/06

Keywords

  • Stokes equation
  • iteration step
  • domain decomposition method
  • convergence of numerical methods
  • factorization
  • operations research
  • bi-harmonic
  • convergence behaviors
  • scalar problems

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  • Cite this

    Dolean, V., Nataf, F., & Rapin, G. (2008). How to use the smith factorization for domain decomposition methods applied to the stokes equations. In Domain Decomposition Methods in Science and Engineering XVII (Vol. 60, pp. 477-484). (Lecture Notes in Computational Science and Engineering; Vol. 60). Springer. https://doi.org/10.1007/978-3-540-75199-1_60