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dc.contributor.authorPetras, A.
dc.contributor.authorLing, L.
dc.contributor.authorRuuth, S.J.
dc.description.abstractPartial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method for solving PDEs on surfaces using standard finite difference schemes. In this paper, we formulate an explicit closest point method using finite difference schemes derived from radial basis functions (RBF-FD). Unlike the orthogonal gradients method (Piret, J. Comput. Phys. 231(14):4662-4675, [2012]), our proposed method uses RBF centers on regular grid nodes. This formulation not only reduces the computational cost but also avoids the ill-conditioning from point clustering on the surface and is more natural to couple with a grid based manifold evolution algorithm (Leung and Zhao, J. Comput. Phys. 228(8):2993-3024, [2009]). When compared to the standard finite difference discretization of the closest point method, the proposed method requires a smaller computational domain surrounding the surface, resulting in a decrease in the number of sampling points on the surface. In addition, higher-order schemes can easily be constructed by increasing the number of points in the RBF-FD stencil. Applications to a variety of examples are provided to illustrate the numerical convergence of the method.en_US
dc.description.sponsorshipNSERC Canada (RGPIN 227823), Hong Kong Research Grant Council GRF Grant (HKBU 11528205), Hong Kong Baptist University FRG Grant.en_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectclosest point methoden_US
dc.subjectembedding methoden_US
dc.subjectradial basis functionsen_US
dc.subjectfinite differencesen_US
dc.titleAn RBF-FD closest point method for solving PDEs on surfacesen_US
dc.journal.titleJournal of Computational Physicsen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España