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)

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.

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

Fingerprint

Domain decomposition methods
Stokes Equations
Domain Decomposition Method
Factorization
Biharmonic
Scalar
Stokes System
Stokes Problem
Two-dimensional Systems
Demonstrate

Keywords

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

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
Dolean, Victorita ; Nataf, Frédéric ; Rapin, Gerd. / How to use the smith factorization for domain decomposition methods applied to the stokes equations. Domain Decomposition Methods in Science and Engineering XVII. Vol. 60 Springer, 2008. pp. 477-484 (Lecture Notes in Computational Science and Engineering).
@inproceedings{395e653b2ab64938ac26d3df36434f84,
title = "How to use the smith factorization for domain decomposition methods applied to the stokes equations",
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.",
keywords = "Stokes equation, iteration step, domain decomposition method, convergence of numerical methods, factorization, operations research, bi-harmonic, convergence behaviors, scalar problems",
author = "Victorita Dolean and Fr{\'e}d{\'e}ric Nataf and Gerd Rapin",
year = "2008",
month = "12",
day = "1",
doi = "10.1007/978-3-540-75199-1_60",
language = "English",
isbn = "9783540751984",
volume = "60",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer",
pages = "477--484",
booktitle = "Domain Decomposition Methods in Science and Engineering XVII",

}

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, Lecture Notes in Computational Science and Engineering, vol. 60, Springer, pp. 477-484, 17th International Conference on Domain Decomposition Methods, St. Wolfgang /Strobl, Austria, 3/07/06. https://doi.org/10.1007/978-3-540-75199-1_60

How to use the smith factorization for domain decomposition methods applied to the stokes equations. / Dolean, Victorita; Nataf, Frédéric; Rapin, Gerd.

Domain Decomposition Methods in Science and Engineering XVII. Vol. 60 Springer, 2008. p. 477-484 (Lecture Notes in Computational Science and Engineering; Vol. 60).

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

TY - GEN

T1 - How to use the smith factorization for domain decomposition methods applied to the stokes equations

AU - Dolean, Victorita

AU - Nataf, Frédéric

AU - Rapin, Gerd

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

KW - Stokes equation

KW - iteration step

KW - domain decomposition method

KW - convergence of numerical methods

KW - factorization

KW - operations research

KW - bi-harmonic

KW - convergence behaviors

KW - scalar problems

UR - http://www.scopus.com/inward/record.url?scp=78651523813&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-75199-1_60

DO - 10.1007/978-3-540-75199-1_60

M3 - Conference contribution book

SN - 9783540751984

VL - 60

T3 - Lecture Notes in Computational Science and Engineering

SP - 477

EP - 484

BT - Domain Decomposition Methods in Science and Engineering XVII

PB - Springer

ER -

Dolean V, Nataf F, Rapin G. 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. Springer. 2008. p. 477-484. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-540-75199-1_60