Optimality of the method of fundamental solutions

Kwun Ying Wong, Leevan LING*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)
4 Downloads (Pure)

Abstract

The Effective-Condition-Number (ECN) is a sensitivity measure for a linear system; it differs from the traditional condition-number in the sense that the ECN is also right-hand side vector dependent. The first part of this work, in [EABE 33(5): 637-43], revealed the close connection between the ECN and the accuracy of the Method of Fundamental Solutions (MFS) for each given problem. In this paper, we show how the ECN can help achieve the problem-dependent quasi-optimal settings for MFS calculationsthat is, determining the position and density of the source points. A series of examples on Dirichlet and mixed boundary conditions shows the reliability of the proposed scheme; whenever the MFS fails, the corresponding value of the ECN strongly indicates to the user to switch to other numerical methods.

Original languageEnglish
Pages (from-to)42-46
Number of pages5
JournalEngineering Analysis with Boundary Elements
Volume35
Issue number1
DOIs
Publication statusPublished - Jan 2011

Scopus Subject Areas

  • Analysis
  • Engineering(all)
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Effective-condition-number
  • Laplace equation
  • MFS

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