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

Handle URI:
http://hdl.handle.net/10754/597872
Title:
Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator
Authors:
Bonito, Andrea; Pasciak, Joseph E.
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.
Citation:
Bonito 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.
Publisher:
American Mathematical Society (AMS)
Journal:
Mathematics of Computation
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
1-Sep-2012
DOI:
10.1090/s0025-5718-2011-02551-2
Type:
Article
ISSN:
0025-5718; 1088-6842
Sponsors:
This 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.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBonito, Andreaen
dc.contributor.authorPasciak, Joseph E.en
dc.date.accessioned2016-02-25T12:58:09Zen
dc.date.available2016-02-25T12:58:09Zen
dc.date.issued2012-09-01en
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.en
dc.identifier.issn0025-5718en
dc.identifier.issn1088-6842en
dc.identifier.doi10.1090/s0025-5718-2011-02551-2en
dc.identifier.urihttp://hdl.handle.net/10754/597872en
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.en
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.en
dc.publisherAmerican Mathematical Society (AMS)en
dc.titleConvergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operatoren
dc.typeArticleen
dc.identifier.journalMathematics of Computationen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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