Department of Mathematics
A localized meshless method for diffusion on folded surfaces
© 2015 Elsevier Inc. 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
Link to Publisher's Edition
Cheung, Ka Chun, Leevan Ling, and Steven J. Ruuth. "A localized meshless method for diffusion on folded surfaces." Journal of Computational Physics 297 (2015): 194-206.