Improved numerical solver for Kansa's method based on affine space decomposition

Leevan LING*, Y. C. Hon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)

Abstract

Radial Basis functions (RBFs) have been successfully developed as a truly mesh-free method to find the numerical solutions of partial differential equations (PDEs). In particular, the asymmetric RBF collocation method (Kansa's method) is one of the most frequently used methods due to its ease of implementation. To achieve high accuracy, the resultant system of RBF-PDE problem usually becomes badly conditioned. We propose in this paper an improved solution method based on an affine space decomposition that decouples the influence between the interior and boundary collocations. Numerical examples are given to compare the proposed method with several direct methods.

Original languageEnglish
Pages (from-to)1077-1085
Number of pages9
JournalEngineering Analysis with Boundary Elements
Volume29
Issue number12
DOIs
Publication statusPublished - Dec 2005

Scopus Subject Areas

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

User-Defined Keywords

  • Collocation
  • Partial differential equation
  • Radial basis function

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