A numerical scheme based on local integrated RBFNs and Cartesian grids for solving second-order elliptic problems in two dimensions

Mai-Duy, Nam and Tran-Cong, Thanh (2010) A numerical scheme based on local integrated RBFNs and Cartesian grids for solving second-order elliptic problems in two dimensions. In: Recent studies in meshless and other novel computational methods. Tech Science Press, Duluth, GA. United States, pp. 17-33. ISBN 0-9824205-4-4

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Abstract

This paper reports a new Cartesian-grid computational technique, based on local integrated radialbasis- 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. Numerical experiments indicate that the latter outperforms the former regarding accuracy. Moreover, the proposed local IRBFN CV method 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: Book Chapter (Commonwealth Reporting Category B)
Refereed: Yes
Item Status: Live Archive
Additional Information: © Tech Science Press 2010. Held USQ Library 519.5 Rec
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 18 Mar 2011 05:31
Last Modified: 11 Nov 2013 23:19
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
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
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/18255

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