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dc.contributor.authorBonito, Andrea
dc.contributor.authorPasciak, Joseph E.
dc.date.accessioned2016-02-25T12:58:09Z
dc.date.available2016-02-25T12:58:09Z
dc.date.issued2012-09-01
dc.identifier.citationBonito A, Pasciak JE (2012) Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator. Math Comp 81: 1263–1288. Available: http://dx.doi.org/10.1090/s0025-5718-2011-02551-2.
dc.identifier.issn0025-5718
dc.identifier.issn1088-6842
dc.identifier.doi10.1090/s0025-5718-2011-02551-2
dc.identifier.urihttp://hdl.handle.net/10754/597872
dc.description.abstractWe 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.
dc.description.sponsorshipThis work was supported in part by award number KUS-C1-016-04 made by KingAbdulla University of Science and Technology (KAUST). The first author was alsosupported in part by the National Science Foundation through Grant DMS-0914977while the second was also supported in part by the National Science Foundationthrough Grant DMS-0609544.
dc.publisherAmerican Mathematical Society (AMS)
dc.titleConvergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator
dc.typeArticle
dc.identifier.journalMathematics of Computation
dc.contributor.institutionTexas A and M University, College Station, United States
kaust.grant.numberKUS-C1-016-04


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