Department of Mathematics
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.
Closest point method, Diffusion, Power function, Radial basis function (RBF), Surface
Source Publication Title
Journal of Computational Physics
Copyright © 2015 Elsevier Inc. All rights reserved.
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.
Link to Publisher's Edition
Cheung, K., Ling, L., & Ruuth, S. (2015). A localized meshless method for diffusion on folded surfaces. Journal of Computational Physics, 297, 194-206. https://doi.org/10.1016/j.jcp.2015.05.021