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

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    Type
    Article
    Authors
    Piret, Cécile
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2012-05
    Permanent link to this record
    http://hdl.handle.net/10754/599943
    
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    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.
    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).
    Publisher
    Elsevier BV
    Journal
    Journal of Computational Physics
    DOI
    10.1016/j.jcp.2012.03.007
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2012.03.007
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