The method of transformed angular basis function for solving the Laplace equation

Xinxiang Li, Jaeyoun Oh, Yong Wang, Huiqing Zhu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this paper, we propose a new approach to improve the method of angular basis function (MABF) proposed by Young et al. (2015) for the Laplace equation in two-dimensional settings. Instead of the fundamental solution ln r used in the traditional Method of Fundamental Solution (MFS), MABF employs a different basis function θ and produces good approximate solutions on the domains with acute, narrow regions and exterior problems (Young et al., 2015). However, the definition of θ inevitably incurs a singularity situation for many different types of domains. Therefore, the selection of source points of MABF is not as convenient as the traditional MFS. To avoid the singularity situation in implementing, we introduce a transformation so that the transformed angular basis function does not exhibit this type of singularity for commonly used distributions of source points. As a result, source points for the method of transformed angular basis function (MTABF) can then be chosen in a similar way to traditional MFS. Numerical experiments demonstrate that the proposed approach significantly simplifies the selection of source points in MABF for different types of domains, which makes MABF more applicable. Numerical results of MTABF and MFS are presented for comparison purposes.

Original languageEnglish
Pages (from-to)72-82
Number of pages11
JournalEngineering Analysis with Boundary Elements
StatePublished - Aug 2018


  • Angular basis functions
  • Method of fundamental solution
  • Transformed angular basis functions


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