On a local Fourier analysis for overlapping block smoothers on triangular grids

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• 作者：C. Rodrigo ; ^{carmenr@unizar.es" class="auth_mail" title="E-mail the corresponding author} ; F.J. Gaspar ; F.J. Lisbona
• 关键词：Multigrid ; Triangular grids ; Overlapping block smoothers ; Box-relaxation ; Vanka smoothers ; Local Fourier analysis ; Saddle point type problems ; Stokes ; Né ; dé ; lec
• 刊名：Applied Numerical Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：105
• 期：Complete
• 页码：96-111
• 全文大小：526 K

文摘

A general local Fourier analysis for overlapping block smoothers on triangular grids is presented. This analysis is explained in a general form for its application to problems with different discretizations. This tool is demonstrated for two different problems: a stabilized linear finite element discretization of Stokes equations and an edge-based discretization of the curl–curl operator by lowest-order Nédélec finite element method. In this latter, special Fourier modes have to be considered in order to perform the analysis. Numerical results comparing two- and three-grid convergence factors predicted by the local Fourier analysis to real asymptotic convergence factors are presented to confirm the predictions of the analysis and show their usefulness.