Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On approximate cardinal preconditioning methods for solving PDEs with radial basis functions

Language

English

Abstract

The approximate cardinal basis function (ACBF) preconditioning technique has been used to solve partial differential equations (PDEs) with radial basis functions (RBFs). In [Ling L, Kansa EJ. A least-squares preconditioner for radial basis functions collocation methods. Adv Comput Math; in press], a preconditioning scheme that is based upon constructing the least-squares approximate cardinal basis function from linear combinations of the RBF-PDE matrix elements has shown very attractive numerical results. This preconditioning technique is sufficiently general that it can be easily applied to many differential operators. In this paper, we review the ACBF preconditioning techniques previously used for interpolation problems and investigate a class of preconditioners based on the one proposed in [Ling L, Kansa EJ. A least-squares preconditioner for radial basis functions collocation methods. Adv Comput Math; in press] when a cardinality condition is enforced on different subsets. We numerically compare the ACBF preconditioners on several numerical examples of Poisson's, modified Helmholtz and Helmholtz equations, as well as a diffusion equation and discuss their performance. © 2005 Elsevier Ltd. All rights reserved.

Keywords

Cardinal basis function, Partial differential equation, Preconditioner, Radial basis function

Publication Date

2005

Source Publication Title

Engineering Analysis with Boundary Elements

Volume

29

Issue

4

Start Page

343

End Page

353

Publisher

Elsevier

DOI

10.1016/j.enganabound.2004.05.006

ISSN (print)

09557997

This document is currently not available here.

Share

COinS