Efficient geometric multigrid implementation for triangular grids

Authors:
Francisco Gaspar;J. L. Gracia;F. J. Lisbona;C. Rodrigo
Affiliations:
Department of Applied Mathematics, University of Zaragoza, Spain;Department of Applied Mathematics, University of Zaragoza, Spain;Department of Applied Mathematics, University of Zaragoza, Spain;Department of Applied Mathematics, University of Zaragoza, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

This paper deals with a stencil-based implementation of a geometric multigrid method on semi-structured triangular grids (triangulations obtained by regular refinement of an irregular coarse triangulation) for linear finite element methods. An efficient and elegant procedure to construct these stencils using a reference stencil associated to a canonical hexagon is proposed. Local Fourier Analysis (LFA) is applied to obtain asymptotic convergence estimates. Numerical experiments are presented to illustrate the efficiency of this geometric multigrid algorithm, which is based on a three-color smoother.