A localized meshless method for diffusion on folded surfaces

Ka Chun Cheung*, Leevan LING, Steven J. Ruuth

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)194-206
Number of pages13
JournalJournal of Computational Physics
Volume297
DOIs
Publication statusPublished - 5 Sep 2015

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

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

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