A Cartesian-grid collocation method based on radial-basis-function networks for solving PDEs in irregular domains

Mai-Duy, Nam and Tran-Cong, Thanh (2007) A Cartesian-grid collocation method based on radial-basis-function networks for solving PDEs in irregular domains. Numerical Methods for Partial Differential Equations, 23 (5). pp. 1192-1210. ISSN 0749-159X

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Abstract

[Abstract]: This paper reports a new Cartesian-grid collocation method based on radial-basis-function networks (RBFNs) for numerically solving elliptic partial differential equations (PDEs) 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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author's Orignal deposited in accordance with the copyright policy of the publisher.
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 07 Feb 2008 05:58
Last Modified: 02 Jul 2013 22:54
Uncontrolled Keywords: integrated radial-basis-function network, collocation method, Cartesian grid, irregular domain
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
Identification Number or DOI: doi: 10.1002/num.20217
URI: http://eprints.usq.edu.au/id/eprint/3569

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