A Cartesian-grid discretisation scheme based on local integrated RBFNs for two-dimensional elliptic problems

Mai-Duy, Nam and Tran-Cong, Thanh (2009) A Cartesian-grid discretisation scheme based on local integrated RBFNs for two-dimensional elliptic problems. CMES: Computer Modeling in Engineering and Sciences, 51 (3). pp. 213-238. ISSN 1526-1492

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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Depositing User: Prof Thanh Tran-Cong
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 28 Jun 2010 01:17
Last Modified: 02 Jul 2013 23:39
Uncontrolled Keywords: local approximations; integrated RBFNs; point collocation; subregion collocation; second-order differential problems
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: doi: 10.3970/cmes.2009.051.213
URI: http://eprints.usq.edu.au/id/eprint/6903

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