Computing eigenmodes of elliptic operators using radial basis functions

R. B. Platte, T. A. Driscoll

Research output: Contribution to journalArticle

57 Scopus citations

Abstract

Radial basis function (RBF) approximations have been successfully used to solve boundary-value problems numerically. We show that RBFs can also be used to compute eigenmodes of elliptic operators. Particular attention is given to the Laplacian operator in two dimensions, including techniques to avoid degradation of the solution near the boundaries. For regions with corner singularities, special functions must be added to the basis to maintain good convergence. Numerical results compare favorably to basic finite-element methods.

Original languageEnglish (US)
Pages (from-to)561-576
Number of pages16
JournalComputers and Mathematics with Applications
Volume48
Issue number3-4
DOIs
StatePublished - Aug 1 2004
Externally publishedYes

Keywords

  • Corner singularities
  • Eigenvalues
  • Laplacian
  • Numerical methods
  • Radial basis functions

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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