Analysis of aggregation-based multigrid

被引:31
作者
Muresan, Adrian C. [1 ]
Notay, Yvan [2 ]
机构
[1] Romanian Acad, T Popoviciu Inst Numer Anal, Cluj Napoca 400110, Romania
[2] Univ Libre Bruxelles, Serv Metrol Nucleaire, B-1050 Brussels, Belgium
关键词
multigrid; aggregation; Fourier analysis; Krylov subspace method; conjugate gradient; preconditioning;
D O I
10.1137/060678397
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Aggregation-based multigrid with standard piecewise constant like prolongation is investigated. Unknowns are aggregated either by pairs or by quadruplets; in the latter case the grouping may be either linewise or boxwise. A Fourier analysis is developed for a model two-dimensional anisotropic problem. Most of the results are stated for an arbitrary smoother (which fits with the Fourier analysis framework). It turns out that the convergence factor of two-grid schemes can be bounded independently of the grid size. With a sensible choice of the (linewise or boxwise) coarsening, the bound is also uniform with respect to the anisotropy ratio, without requiring a specialized smoother. The bound is too large to guarantee optimal convergence properties with the V-cycle or the standard W-cycle, but a W-cycle scheme accelerated by the recursive use of the conjugate gradient method exhibits near grid independent convergence.
引用
收藏
页码:1082 / 1103
页数:22
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