The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

Handle URI:
http://hdl.handle.net/10754/599943
Title:
The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces
Authors:
Piret, Cécile
Abstract:
Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in . R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time. © 2012 Elsevier Inc.
Citation:
Piret C (2012) The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces. Journal of Computational Physics 231: 4662–4675. Available: http://dx.doi.org/10.1016/j.jcp.2012.03.007.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
May-2012
DOI:
10.1016/j.jcp.2012.03.007
Type:
Article
ISSN:
0021-9991
Sponsors:
The work of this author was supported by a FSR post-doctoral grant from the catholic University of Louvain. Part of the present work was conducted when the author was a Visiting Post-Doctoral Research Assistant at OCCAM (Oxford Centre for Collaborative Applied Mathematics) under support provided by Award No. KUK-C1-013-04 to the University of Oxford, UK, by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorPiret, Cécileen
dc.date.accessioned2016-02-28T06:32:57Zen
dc.date.available2016-02-28T06:32:57Zen
dc.date.issued2012-05en
dc.identifier.citationPiret C (2012) The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces. Journal of Computational Physics 231: 4662–4675. Available: http://dx.doi.org/10.1016/j.jcp.2012.03.007.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2012.03.007en
dc.identifier.urihttp://hdl.handle.net/10754/599943en
dc.description.abstractMuch work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in . R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time. © 2012 Elsevier Inc.en
dc.description.sponsorshipThe work of this author was supported by a FSR post-doctoral grant from the catholic University of Louvain. Part of the present work was conducted when the author was a Visiting Post-Doctoral Research Assistant at OCCAM (Oxford Centre for Collaborative Applied Mathematics) under support provided by Award No. KUK-C1-013-04 to the University of Oxford, UK, by King Abdullah University of Science and Technology (KAUST).en
dc.publisherElsevier BVen
dc.subjectClosest point methoden
dc.subjectImplicit surfacesen
dc.subjectLevel set methoden
dc.subjectOGr methoden
dc.subjectOrthogonal gradients methoden
dc.subjectRadial basis functionsen
dc.subjectRBFen
dc.titleThe orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfacesen
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionUniversite Catholique de Louvain, Louvain-la-Neuve, Belgiumen
kaust.grant.numberKUK-C1-013-04en
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