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

被引：7

作者：

Wu, Yongke ^{[2
]}

Chen, Long ^{[1
]}

Xie, Xiaoping ^{[2
]}

Xu, Jinchao ^{[3
,4
,5
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[2] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

[3] Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China

[4] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

[5] Penn State Univ, University Pk, PA 16801 USA

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2012年 / 32卷 / 04期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

bilinear element; anisotropic equations; multigrid method; ITERATIVE METHODS; ALGORITHMS;

D O I：

10.1093/imanum/drr043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1329 / 1347

页数：19

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