http://dx.doi.org/10.1016/j.mcm.2005.01.002">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Preconditioning for radial basis functions with domain decomposition methods

Language

English

Abstract

In our previous work, an effective preconditioning scheme that is based upon constructing least-squares approximation cardinal basis functions (ACBFs) from linear combinations of the RBF-PDE matrix elements has shown very attractive numerical results. The preconditioner costs O(N2) flops to set up and O(N) storage. The preconditioning technique is sufficiently general that it can be applied to different types of different operators. This was applied to the 2D multiquadric method, with c∼1/√N on the Poisson test problem, the preconditioned GMRES converges in tens of iterations. In this paper, we combine the RBF methods and the ACBF preconditioning technique with the domain decomposition method (DDM). We studied different implementations of the ACBF-DDM scheme and provide numerical results for N > 10,000 nodes. We shall demonstrate that the efficiency of the ACBF-DDM scheme improves dramatically as successively finer partitions of the domain are considered. © 2005 Elsevier Ltd. All rights reserved.

Keywords

Approximate cardinal basis function, Domain decomposition, Partial differential equation, Preconditioner, Radial basis function

Publication Date

2004

Source Publication Title

Mathematical and Computer Modelling

Volume

40

Issue

13

Start Page

1413

End Page

1427

Publisher

Elsevier

ISSN (print)

08957177

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