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dc.contributor.authorPetras, A.
dc.contributor.authorLing, L.
dc.contributor.authorPiret, C.
dc.contributor.authorRuuth, S.J.
dc.description.abstractThe closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation of the surface and standard Cartesian grid methods in the embedding space. Recently, a closest point method with explicit time-stepping was proposed that uses finite differences derived from radial basis functions (RBF-FD). Here, we propose a least-squares implicit formulation of the closest point method to impose the constant-along-normal extension of the solution on the surface into the embedding space. Our proposed method is particularly flexible with respect to the choice of the computational grid in the embedding space. In particular, we may compute over a computational tube that contains problematic nodes. This fact enables us to combine the proposed method with the grid based particle method (Leung and Zhao, J. Comput. Phys. 228(8):2993-3024, [2009]) to obtain a numerical method for approximating PDEs on moving surfaces. We present a number of examples to illustrate the numerical convergence properties of our proposed method. Experiments for advection-diffusion equations and Cahn-Hilliard equations that are strongly coupled to the velocity of the surface are also presented.en_US
dc.description.sponsorshipNSERC Canada Grant (RGPIN 2016-04361), Hong Kong Research Grant Council GRF Grant, Hong Kong Baptist University FRG Granten_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectpartial differential equations on moving surfacesen_US
dc.subjectclosest point methoden_US
dc.subjectgrid based particle methoden_US
dc.subjectradial basis functions finite differences (RBF-FD)en_US
dc.subjectleast-squares methoden_US
dc.titleA least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfacesen_US
dc.journal.titleJournal of Computational Physicsen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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