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A Cartesian-Grid Discretisation Scheme Based on Local Integrated RBFNs for Two-Dimensional Elliptic Problems

N. Mai-Duy1, T. Tran-Cong1
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, University of Southern Queensland, Toowoomba, QLD 4350, Australia.

Computer Modeling in Engineering & Sciences 2009, 51(3), 213-238. https://doi.org/10.3970/cmes.2009.051.213

Abstract

This paper reports a new numerical scheme based on Cartesian grids and local integrated radial-basis-function networks (IRBFNs) for the solution of second-order elliptic differential problems defined on two-dimensional regular and irregular domains. At each grid point, only neighbouring nodes are activated to construct the IRBFN approximations. Local IRBFNs are introduced into two different schemes for discretisation of partial differential equations, namely point collocation and control-volume (CV)/subregion-collocation. Linear (e.g. heat flow) and nonlinear (e.g. lid-driven triangular-cavity fluid flow) problems are considered. Numerical results indicate that the local IRBFN CV scheme outperforms the local IRBFN point-collocation scheme regarding accuracy. Moreover, the former shows a similar level of the matrix condition number and a significant improvement in accuracy over a linear CV method.

Keywords

local approximations, integrated RBFNs, point collocation, subregion collocation, second-order differential problems.

Cite This Article

Mai-Duy, N., Tran-Cong, T. (2009). A Cartesian-Grid Discretisation Scheme Based on Local Integrated RBFNs for Two-Dimensional Elliptic Problems. CMES-Computer Modeling in Engineering & Sciences, 51(3), 213–238.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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