dc.contributor.author Chen, Yujia dc.contributor.author Macdonald, Colin B. dc.date.accessioned 2016-02-28T06:31:42Z dc.date.available 2016-02-28T06:31:42Z dc.date.issued 2015-01 dc.identifier.citation Chen 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.issn 1064-8275 dc.identifier.issn 1095-7197 dc.identifier.doi 10.1137/130929497 dc.identifier.uri http://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.sponsorship This work was supported by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). dc.publisher Society for Industrial & Applied Mathematics (SIAM) dc.subject Closest point method dc.subject Geometric multigrid method dc.subject Laplace-Beltrami operator dc.subject Surface elliptic problem dc.subject Surface Poisson problem dc.title The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces dc.type Article dc.identifier.journal SIAM Journal on Scientific Computing dc.contributor.institution University of Oxford, Oxford, United Kingdom kaust.grant.number KUK-C1-013-04
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