A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations

Michele Benzi; Michael Ng; Qiang Niu; Zhen Wang

doi:10.1016/j.jcp.2011.04.001

A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations

Michele Benzi^*, Michael Ng, Qiang Niu, Zhen Wang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

96 Citations (Scopus)

Abstract

In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo [7]. Numerical results for a variety of finite element discretizations of both steady and unsteady incompressible flow problems indicate very good behavior of the RDF preconditioner with respect to both mesh size and viscosity.

Original language	English
Pages (from-to)	6185-6202
Number of pages	18
Journal	Journal of Computational Physics
Volume	230
Issue number	16
DOIs	https://doi.org/10.1016/j.jcp.2011.04.001
Publication status	Published - 10 Jul 2011

User-Defined Keywords

Dimensional Factorization
Dimensional Splitting
Krylov subspace method
Navier-Stokes equations
Oseen problem
Saddle point problem

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10.1016/j.jcp.2011.04.001

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@article{7c4f1259056a41aa86b7afcb98e81a1a,

title = "A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations",

abstract = "In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo [7]. Numerical results for a variety of finite element discretizations of both steady and unsteady incompressible flow problems indicate very good behavior of the RDF preconditioner with respect to both mesh size and viscosity.",

keywords = "Dimensional Factorization, Dimensional Splitting, Krylov subspace method, Navier-Stokes equations, Oseen problem, Saddle point problem",

author = "Michele Benzi and Michael Ng and Qiang Niu and Zhen Wang",

note = "Funding Information: Michele Benzi{\textquoteright}s work was supported in part by a grant from the University Research Council of Emory University. Michael Ng{\textquoteright}s work was supported in part by HKRGC grants and HKBU FRGs. Qiang Niu{\textquoteright}s work was supported in part by the UIC research fund and XJTLU research fund. The authors are indebted to the three anonymous referees for many constructive comments and suggestions.",

year = "2011",

month = jul,

day = "10",

doi = "10.1016/j.jcp.2011.04.001",

language = "English",

volume = "230",

pages = "6185--6202",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations

AU - Benzi, Michele

AU - Ng, Michael

AU - Niu, Qiang

AU - Wang, Zhen

N1 - Funding Information: Michele Benzi’s work was supported in part by a grant from the University Research Council of Emory University. Michael Ng’s work was supported in part by HKRGC grants and HKBU FRGs. Qiang Niu’s work was supported in part by the UIC research fund and XJTLU research fund. The authors are indebted to the three anonymous referees for many constructive comments and suggestions.

PY - 2011/7/10

Y1 - 2011/7/10

N2 - In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo [7]. Numerical results for a variety of finite element discretizations of both steady and unsteady incompressible flow problems indicate very good behavior of the RDF preconditioner with respect to both mesh size and viscosity.

AB - In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo [7]. Numerical results for a variety of finite element discretizations of both steady and unsteady incompressible flow problems indicate very good behavior of the RDF preconditioner with respect to both mesh size and viscosity.

KW - Dimensional Factorization

KW - Dimensional Splitting

KW - Krylov subspace method

KW - Navier-Stokes equations

KW - Oseen problem

KW - Saddle point problem

UR - http://www.scopus.com/inward/record.url?scp=79957551863&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2011.04.001

DO - 10.1016/j.jcp.2011.04.001

M3 - Journal article

AN - SCOPUS:79957551863

SN - 0021-9991

VL - 230

SP - 6185

EP - 6202

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 16

ER -

A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations

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