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

Cécile Piret

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)4662-4675
Number of pages14
JournalJournal of Computational Physics
Volume231
Issue number14
DOIs
StatePublished - May 2012
Externally publishedYes

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