Boundary solution of Poisson's equation using radial basis function collocated on Gaussian quadrature nodes

Citation
M. Elansari et al., Boundary solution of Poisson's equation using radial basis function collocated on Gaussian quadrature nodes, COMMUN NUM, 17(7), 2001, pp. 455-464
Citations number
17
Categorie Soggetti
Engineering Mathematics
Journal title
COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING
ISSN journal
10698299 → ACNP
Volume
17
Issue
7
Year of publication
2001
Pages
455 - 464
Database
ISI
SICI code
1069-8299(200107)17:7<455:BSOPEU>2.0.ZU;2-B
Abstract
In the solution of Poisson's equation using either the dual reciprocity bou ndary element method or the method of fundamental solution, radial basis fu nctions (RBFs) are used to approximate the right-hand side of the governing partial differential equation to eliminate the domain integration. This pa per shows that if the RBF interpolation is collocated on the Gaussian quadr ature nodes, we seem to observe superconvergence behaviour. This behaviour is demonstrated using a series of numerical examples. Copyright (C) 2001 Jo hn Wiley & Sons, Ltd.