Convergence rate estimate for a domain decomposition method

Xiao Chuan Cai; William D. Gropp; David E. Keyes

doi:10.1007/BF01385503

Convergence rate estimate for a domain decomposition method

Xiao Chuan Cai^*, William D. Gropp, David E. Keyes

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ℝ². We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.

Original language	English (US)
Pages (from-to)	153-169
Number of pages	17
Journal	Numerische Mathematik
Volume	61
Issue number	1
DOIs	https://doi.org/10.1007/BF01385503
State	Published - Dec 1992
Externally published	Yes

Keywords

Mathematics Subject Classification (1991): 65N30, 65F10

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/BF01385503

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title = "Convergence rate estimate for a domain decomposition method",

abstract = "We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ℝ2. We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.",

keywords = "Mathematics Subject Classification (1991): 65N30, 65F10",

author = "Cai, {Xiao Chuan} and Gropp, {William D.} and Keyes, {David E.}",

year = "1992",

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pages = "153--169",

journal = "Numerische Mathematik",

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T1 - Convergence rate estimate for a domain decomposition method

AU - Cai, Xiao Chuan

AU - Gropp, William D.

AU - Keyes, David E.

PY - 1992/12

Y1 - 1992/12

N2 - We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ℝ2. We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.

AB - We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ℝ2. We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.

KW - Mathematics Subject Classification (1991): 65N30, 65F10

UR - http://www.scopus.com/inward/record.url?scp=0040132047&partnerID=8YFLogxK

U2 - 10.1007/BF01385503

DO - 10.1007/BF01385503

M3 - Article

AN - SCOPUS:0040132047

SN - 0029-599X

VL - 61

SP - 153

EP - 169

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 1

ER -

Convergence rate estimate for a domain decomposition method

Abstract

Keywords

ASJC Scopus subject areas

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