Circulant block-factorization preconditioning of anisotropic elliptic problems

I. D. Lirkov; S. D. Margenov; L. T. Zikatanov

doi:10.1007/BF02684392

Circulant block-factorization preconditioning of anisotropic elliptic problems

I. D. Lirkov
, S. D. Margenov
, L. T. Zikatanov

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

6 Scopus citations

Abstract

The recently introduced circulant block-factorization preconditioners are studied in this paper. The general approach is first formulated for the case of block-tridiagonal sparse matrices. Then an estimate of the condition number of the preconditioned matrix for a model anisotropic Dirichlet boundary value problem is derived in the form κ < √2ε(n + 1) + 2, where N = n² is the size of the discrete problem, and ε stands for the ratio of the anisotropy. Various numerical tests demonstrating the behavior of the circulant block-factorization preconditioners for anisotropic problems are presented.

Original language	English (US)
Pages (from-to)	245-258
Number of pages	14
Journal	Computing (Vienna/New York)
Volume	58
Issue number	3
DOIs	https://doi.org/10.1007/BF02684392
State	Published - 1997

All Science Journal Classification (ASJC) codes

Software
Theoretical Computer Science
Numerical Analysis
Computer Science Applications
Computational Theory and Mathematics
Computational Mathematics

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10.1007/BF02684392

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abstract = "The recently introduced circulant block-factorization preconditioners are studied in this paper. The general approach is first formulated for the case of block-tridiagonal sparse matrices. Then an estimate of the condition number of the preconditioned matrix for a model anisotropic Dirichlet boundary value problem is derived in the form κ < √2ε(n + 1) + 2, where N = n2 is the size of the discrete problem, and ε stands for the ratio of the anisotropy. Various numerical tests demonstrating the behavior of the circulant block-factorization preconditioners for anisotropic problems are presented.",

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journal = "Computing (Vienna/New York)",

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AU - Margenov, S. D.

AU - Zikatanov, L. T.

PY - 1997

Y1 - 1997

N2 - The recently introduced circulant block-factorization preconditioners are studied in this paper. The general approach is first formulated for the case of block-tridiagonal sparse matrices. Then an estimate of the condition number of the preconditioned matrix for a model anisotropic Dirichlet boundary value problem is derived in the form κ < √2ε(n + 1) + 2, where N = n2 is the size of the discrete problem, and ε stands for the ratio of the anisotropy. Various numerical tests demonstrating the behavior of the circulant block-factorization preconditioners for anisotropic problems are presented.

AB - The recently introduced circulant block-factorization preconditioners are studied in this paper. The general approach is first formulated for the case of block-tridiagonal sparse matrices. Then an estimate of the condition number of the preconditioned matrix for a model anisotropic Dirichlet boundary value problem is derived in the form κ < √2ε(n + 1) + 2, where N = n2 is the size of the discrete problem, and ε stands for the ratio of the anisotropy. Various numerical tests demonstrating the behavior of the circulant block-factorization preconditioners for anisotropic problems are presented.

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JO - Computing (Vienna/New York)

JF - Computing (Vienna/New York)

IS - 3

ER -

Circulant block-factorization preconditioning of anisotropic elliptic problems

Abstract

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