On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation

Oleg Davydov, Dang Thi Oanh

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39 Citations (Scopus)
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Abstract

We investigate the influence of the shape parameter in the meshless Gaussian RBF finite difference method with irregular centres on the quality of the approximation of the Dirichlet problem for the Poisson equation with smooth solution. Numerical experiments show that the optimal shape parameter strongly depends on the problem, but insignificantly on the density of the centres. Therefore, we suggest a multilevel algorithm that effectively finds near-optimal shape parameter, which helps to significantly reduce the error. Comparison to the finite element method and to the generalised finite differences obtained in the flat limits of the Gaussian RBF is provided.
Original languageEnglish
Pages (from-to)2143-2161
Number of pages19
JournalComputers and Mathematics with Applications
Volume62
Issue number5
DOIs
Publication statusPublished - Sep 2011

Keywords

  • Poisson equation
  • mathematical statisics
  • meshless methods

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