Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

Partial differential equations (PDEs) on surfaces arise in a variety of application areas including biological systems, medical imaging, fluid dynamics, mathematical physics, image processing and computer graphics. In this paper, we propose a radial basis function (RBF) discretization of the closest point method. The corresponding localized meshless method may be used to approximate diffusion on smooth or folded surfaces. Our method has the benefit of having an a priori error bound in terms of percentage of the norm of the solution. A stable solver is used to avoid the ill-conditioning that arises when the radial basis functions (RBFs) become flat.

Keywords

Closest point method, Diffusion, Power function, Radial basis function (RBF), Surface

Publication Date

9-15-2015

Source Publication Title

Journal of Computational Physics

Volume

297

Start Page

194

End Page

206

Publisher

Elsevier

Peer Reviewed

1

Copyright

Copyright © 2015 Elsevier Inc. All rights reserved.

Funder

This project was supported by a CERG Grant of the Research Grants Council, University Grants Committee, Hong Kong, an FRG Grant of HKBU, and a grant from NSERC Canada.

DOI

10.1016/j.jcp.2015.05.021

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.jcp.2015.05.021

ISSN (print)

00219991

Available for download on Sunday, October 01, 2017

Included in

Mathematics Commons

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