A Cartesian‐grid collocation method based on radial‐basis‐function networks for solving PDEs in irregular domains |
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| Authors: | N. Mai‐Duy T. Tran‐Cong |
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| Affiliation: | 1. Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, Queensland 4350, AustraliaFaculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, Queensland 4350, Australia;2. Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, Queensland 4350, Australia |
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| Abstract: | This paper reports a new Cartesian‐grid collocation method based on radial‐basis‐function networks (RBFNs) for numerically solving elliptic partial differential equations in irregular domains. The domain of interest is embedded in a Cartesian grid, and the governing equation is discretized by using a collocation approach. The new features here are (a) one‐dimensional integrated RBFNs are employed to represent the variable along each line of the grid, resulting in a significant improvement of computational efficiency, (b) the present method does not require complicated interpolation techniques for the treatment of Dirichlet boundary conditions in order to achieve a high level of accuracy, and (c) normal derivative boundary conditions are imposed by means of integration constants. The method is verified through the solution of second‐ and fourth‐order PDEs; accurate results and fast convergence rates are obtained. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 |
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| Keywords: | integrated radial‐basis‐function network collocation method Cartesian grid irregular domain |
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