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. 21432161. ISSN 08981221

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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 nearoptimal 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:  29 Jan 2016 14:59 
Related URLs:  
URI:  http://strathprints.strath.ac.uk/id/eprint/36480 
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