Show simple item record

dc.contributor.authorChen, Yujia
dc.contributor.authorMacdonald, Colin B.
dc.date.accessioned2016-02-28T06:31:42Z
dc.date.available2016-02-28T06:31:42Z
dc.date.issued2015-01
dc.identifier.citationChen Y, Macdonald CB (2015) The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces. SIAM Journal on Scientific Computing 37: A134–A155. Available: http://dx.doi.org/10.1137/130929497.
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/130929497
dc.identifier.urihttp://hdl.handle.net/10754/599886
dc.description.abstract© 2015 Society for Industrial and Applied Mathematics. Elliptic partial differential equations are important from both application and analysis points of view. In this paper we apply the closest point method to solve elliptic equations on general curved surfaces. Based on the closest point representation of the underlying surface, we formulate an embedding equation for the surface elliptic problem, then discretize it using standard finite differences and interpolation schemes on banded but uniform Cartesian grids. We prove the convergence of the difference scheme for the Poisson's equation on a smooth closed curve. In order to solve the resulting large sparse linear systems, we propose a specific geometric multigrid method in the setting of the closest point method. Convergence studies in both the accuracy of the difference scheme and the speed of the multigrid algorithm show that our approaches are effective.
dc.description.sponsorshipThis work was supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectClosest point method
dc.subjectGeometric multigrid method
dc.subjectLaplace-Beltrami operator
dc.subjectSurface elliptic problem
dc.subjectSurface Poisson problem
dc.titleThe Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces
dc.typeArticle
dc.identifier.journalSIAM Journal on Scientific Computing
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
kaust.grant.numberKUK-C1-013-04


This item appears in the following Collection(s)

Show simple item record