Multigrid fourier analysis on semi‐structured anisotropic meshes for vector problems
Abstract
An efficient multigrid finite element method for vector problems on triangular anisotropic semi‐structured grids is proposed. This algorithm is based on zebra line‐type smoothers to overcome the difficulties arising when multigrid is applied on stretched meshes. In order to choose the type of multigrid cycle and the number of pre‐ and post‐smoothing steps, a three‐grid Fourier analysis is done. To this end, local Fourier analysis (LFA) on triangular grids for scalar problems is extended to the vector case. To illustrate the good performance of the method, a system of reaction‐diffusion is considered as model problem. A very satisfactory global convergence factor is obtained by using a V(0,2)‐cycle for domains triangulated with highly anisotropic meshes.
First published online: 09 Jun 2011
Keywords:
finite elements, semi‐structured triangular grids, geometric multigrid, local Fourier analysis, three‐grid analysis, anisotropic meshesHow to Cite
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Copyright (c) 2010 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2010 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.