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dc.contributor.authorPiret, Cécile
dc.date.accessioned2016-02-28T06:32:57Z
dc.date.available2016-02-28T06:32:57Z
dc.date.issued2012-05
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.
dc.identifier.issn0021-9991
dc.identifier.doi10.1016/j.jcp.2012.03.007
dc.identifier.urihttp://hdl.handle.net/10754/599943
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.
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).
dc.publisherElsevier BV
dc.subjectClosest point method
dc.subjectImplicit surfaces
dc.subjectLevel set method
dc.subjectOGr method
dc.subjectOrthogonal gradients method
dc.subjectRadial basis functions
dc.subjectRBF
dc.titleThe orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces
dc.typeArticle
dc.identifier.journalJournal of Computational Physics
dc.contributor.institutionUniversite Catholique de Louvain, Louvain-la-Neuve, Belgium
kaust.grant.numberKUK-C1-013-04


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