Mathematical justification for RBF-MFS
type: Item
instance of: scholarly article
title: Mathematical justification for RBF-MFS
zbMATH Open document ID: 1014.65123
DOI: 10.1016/S0955-7997(01)00078-9
author: Jichun Li
published in: Engineering Analysis with Boundary Elements
publication date: 2002-07-03T00:00:00Z
review text: In this note, the radial basis function-method of fundamental solution (RBF-MFS) which couples \textit{E. J. Kansa}'s technique [Comput. Math. Appl. 19, No.~8/9, 147-161 (1990; Zbl 0850.76048)] with the method of fundamental solution are revisited. The idea of RBF-MFS was originally proposed by \textit{M. A. Goldberg} [the numerical evaluation of particular solutions in the BEM -- a review. Boundary Elem. Commun., 99-106 (1995)] and used many engineers later. Here it is shown that the RBF-MFS is theoretically solvable for Hardy's multiquadratics and the cubic radial basis function for the Poisson operator. Numerical results indicate that the RBF-MFS is comparable to Kansa's method.
reviewed by: Wilhelm Heinrichs
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1762684
zbMATH Keywords: radial basis function
zbMATH Keywords: collocation
zbMATH Keywords: dual reciprocity method
zbMATH Keywords: method of fundamental solution
zbMATH Keywords: Kansa's method
zbMATH Keywords: Poisson equation
zbMATH Keywords: comparison of methods
zbMATH Keywords: numerical results
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1762684