Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

An improved subspace selection algorithm for meshless collocation methods

Language

English

Abstract

Choosing data points is a common problem for researchers who employ various meshless methods for solving partial differential equations. On the one hand, high accuracy is always desired; on the other, ill-conditioning problems of the resultant matrices, which may lead to unstable algorithms, prevent some researchers from using meshless methods. For example, the optimal placements of source points in the method of fundamental solutions or of the centers in the radial basis functions method are always unclear. Intuitively, such optimal locations will depend on many factors: the partial differential equations, the domain, the trial basis used (i.e. the employed method itself), the computational precisions, some userdefined parameters, and so on. Such complexity makes the hope of having an optimal centers placement unpromising. In this paper, we provide a data-dependent algorithm that adaptively selects centers based on all the other variables. © 2009 John Wiley & Sons, Ltd.

Keywords

Adaptive greedy algorithm, Collocation, Kansa's method, Radial basis function

Publication Date

2009

Source Publication Title

International Journal for Numerical Methods in Engineering

Volume

80

Issue

13

Start Page

1623

End Page

1639

Publisher

Wiley

DOI

10.1002/nme.2674

Link to Publisher's Edition

http://dx.doi.org/10.1002/nme.2674

ISSN (print)

00295981

ISSN (electronic)

10970207

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