Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator

Andrea Bonito, Joseph E. Pasciak

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We design and analyze variational and non-variational multigrid algorithms for the Laplace-Beltrami operator on a smooth and closed surface. In both cases, a uniform convergence for the V -cycle algorithm is obtained provided the surface geometry is captured well enough by the coarsest grid. The main argument hinges on a perturbation analysis from an auxiliary variational algorithm defined directly on the smooth surface. In addition, the vanishing mean value constraint is imposed on each level, thereby avoiding singular quadratic forms without adding additional computational cost. Numerical results supporting our analysis are reported. In particular, the algorithms perform well even when applied to surfaces with a large aspect ratio. © 2011 American Mathematical Society.
Original languageEnglish (US)
Pages (from-to)1263-1288
Number of pages26
JournalMathematics of Computation
Volume81
Issue number279
DOIs
StatePublished - Sep 1 2012
Externally publishedYes

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