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

Davydov, Oleg and Oanh, Dang Thi (2011) On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation. Computers and Mathematics with Applications, 62 (5). pp. 2143-2161. ISSN 0898-1221

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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.

Item type: Article
ID code: 36480
Keywords: Poisson equation , mathematical statisics, meshless methods, Probabilities. Mathematical statistics
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Pure Administrator
Date Deposited: 19 Dec 2011 11:48
Last modified: 26 Mar 2015 16:44
URI: http://strathprints.strath.ac.uk/id/eprint/36480

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