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An improved subspace selection algorithm for meshless collocation methods
Author(s) -
Ling Leevan,
Schaback Robert
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2674
Subject(s) - collocation (remote sensing) , regularized meshless method , subspace topology , partial differential equation , collocation method , computer science , mathematical optimization , domain (mathematical analysis) , algorithm , selection (genetic algorithm) , mathematics , differential equation , ordinary differential equation , singular boundary method , artificial intelligence , finite element method , machine learning , mathematical analysis , boundary element method , thermodynamics , physics
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 1pt), the computational precisions, some user‐defined 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. Copyright © 2009 John Wiley & Sons, Ltd.