Solving Partial Differential Equations on Surfaces with Fundamental Solutions

Meng Chen, Ka Chun Cheung, Leevan LING*

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingChapterpeer-review


The aim of this paper is to present partial differential equations (PDEs) on surface to the community of methods of fundamental solutions (MFS). First, we present an embedding formulation to embed surface PDEs into a domain so that MFS can be applied after the PDEs is homogenized with a particular solution. Next, we discuss how the domain-MFS method can be used to directly collocate surface PDEs. Some numerical demonstrations were included to study the effect of basis functions and source point locations.

Original languageEnglish
Title of host publicationAdvances in Trefftz Methods and Their Applications
EditorsCarlos Alves, Andreas Karageorghis, Vitor Leitão, Svilen Valtchev
PublisherSpringer Cham
Number of pages11
ISBN (Electronic)9783030528041
ISBN (Print)9783030528065, 9783030528034
Publication statusPublished - 1 Oct 2020

Publication series

NameSEMA SIMAI Springer Series
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X

Scopus Subject Areas

  • Computational Mechanics
  • Numerical Analysis
  • Agricultural and Biological Sciences (miscellaneous)
  • Physics and Astronomy (miscellaneous)
  • Fluid Flow and Transfer Processes
  • Computational Mathematics
  • Industrial and Manufacturing Engineering
  • Applied Mathematics

User-Defined Keywords

  • Collocation
  • Dual reciprocity method
  • Embedding method
  • Laplace-Beltrami


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