Solving eigenvalue problems on curved surfaces using the Closest Point Method

Handle URI:
http://hdl.handle.net/10754/599671
Title:
Solving eigenvalue problems on curved surfaces using the Closest Point Method
Authors:
Macdonald, Colin B.; Brandman, Jeremy; Ruuth, Steven J.
Abstract:
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace-Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach. © 2011 Elsevier Inc.
Citation:
Macdonald CB, Brandman J, Ruuth SJ (2011) Solving eigenvalue problems on curved surfaces using the Closest Point Method. Journal of Computational Physics. Available: http://dx.doi.org/10.1016/j.jcp.2011.06.021.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jun-2011
DOI:
10.1016/j.jcp.2011.06.021
Type:
Article
ISSN:
0021-9991
Sponsors:
The work of this author was supported by an NSERC postdoctoral fellowship, NSF grant No. CCF-0321917, and by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).The work of this author was supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship.The work of this author was partially supported by a Grant from NSERC Canada.
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Full metadata record

DC FieldValue Language
dc.contributor.authorMacdonald, Colin B.en
dc.contributor.authorBrandman, Jeremyen
dc.contributor.authorRuuth, Steven J.en
dc.date.accessioned2016-02-28T06:07:11Zen
dc.date.available2016-02-28T06:07:11Zen
dc.date.issued2011-06en
dc.identifier.citationMacdonald CB, Brandman J, Ruuth SJ (2011) Solving eigenvalue problems on curved surfaces using the Closest Point Method. Journal of Computational Physics. Available: http://dx.doi.org/10.1016/j.jcp.2011.06.021.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2011.06.021en
dc.identifier.urihttp://hdl.handle.net/10754/599671en
dc.description.abstractEigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace-Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach. © 2011 Elsevier Inc.en
dc.description.sponsorshipThe work of this author was supported by an NSERC postdoctoral fellowship, NSF grant No. CCF-0321917, and by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).The work of this author was supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship.The work of this author was partially supported by a Grant from NSERC Canada.en
dc.publisherElsevier BVen
dc.subjectClosest Point Methoden
dc.subjectEigenfunctionsen
dc.subjectEigenvaluesen
dc.subjectImplicit surfacesen
dc.subjectLaplace-Beltrami operatoren
dc.subjectSurface computationen
dc.titleSolving eigenvalue problems on curved surfaces using the Closest Point Methoden
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionCourant Institute of Mathematical Sciences, New York, United Statesen
dc.contributor.institutionSimon Fraser University, Burnaby, Canadaen
kaust.grant.numberKUK-C1-013-04en
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