Convergence analysis of V-Cycle multigrid methods for anisotropic elliptic equations

Yongke Wu, Long Chen, Xiaoping Xie, Jinchao Xu

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Fast multigrid solvers are considered for the linear systems arising from the bilinear finite element discretizations of second-order elliptic equations with anisotropic diffusion. Optimal convergence of Vcycle multigrid methods in the semicoarsening case and nearly optimal convergence of V-cycle multigrid method with line smoothing in the uniformly-coarsening case are established using the Xu-Zikatanov identity. Since the 'regularity assumption' is not used in the analysis, the results can be extended to general domains consisting of rectangles.

Original languageEnglish (US)
Pages (from-to)1329-1347
Number of pages19
JournalIMA Journal of Numerical Analysis
Volume32
Issue number4
DOIs
StatePublished - Oct 1 2012

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Multigrid Method
Coarsening
Convergence Analysis
Elliptic Equations
Linear systems
Cycle
Anisotropic Diffusion
Second Order Elliptic Equations
Finite Element Discretization
Rectangle
Smoothing
Regularity
Linear Systems
Line

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

Cite this

Wu, Yongke ; Chen, Long ; Xie, Xiaoping ; Xu, Jinchao. / Convergence analysis of V-Cycle multigrid methods for anisotropic elliptic equations. In: IMA Journal of Numerical Analysis. 2012 ; Vol. 32, No. 4. pp. 1329-1347.
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Convergence analysis of V-Cycle multigrid methods for anisotropic elliptic equations. / Wu, Yongke; Chen, Long; Xie, Xiaoping; Xu, Jinchao.

In: IMA Journal of Numerical Analysis, Vol. 32, No. 4, 01.10.2012, p. 1329-1347.

Research output: Contribution to journalArticle

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AB - Fast multigrid solvers are considered for the linear systems arising from the bilinear finite element discretizations of second-order elliptic equations with anisotropic diffusion. Optimal convergence of Vcycle multigrid methods in the semicoarsening case and nearly optimal convergence of V-cycle multigrid method with line smoothing in the uniformly-coarsening case are established using the Xu-Zikatanov identity. Since the 'regularity assumption' is not used in the analysis, the results can be extended to general domains consisting of rectangles.

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