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
Recommended Citation
Ling, Leevan, and Robert Schaback. "An improved subspace selection algorithm for meshless collocation methods." International Journal for Numerical Methods in Engineering 80.13 (2009): 1623-1639.