Indirect RBFN method with scattered points for numerical solution of PDEs

Mai-Duy, Nam (2004) Indirect RBFN method with scattered points for numerical solution of PDEs. CMES: Computer Modeling in Engineering and Sciences, 6 (2). pp. 209-226. ISSN 1526-1492

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Abstract

This paper is concerned with the use of the indirect radial basis function network (RBFN) method in solving partial differential equations (PDEs) with scattered points. Indirect RBFNs (Mai-Duy and Tran-Cong, 2001a), which are based on an integration process, are employed to approximate the solution of PDEs via point collocation mechanism in the set of randomly distributed points. The method is tested with the solution of Poisson's equations and the Navier-Stokes equations (Boussinesq material). Good results are obtained using relatively low numbers of data points. For example, the natural convection flow in a square cavity at Rayleigh number of $1.e6$ is simulated successfully using only 1693 random collocation points.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 29 Mar 2010 12:29
Last Modified: 02 Jul 2013 23:44
Uncontrolled Keywords: partial differential equations; indirect RBFN; point collocation
Fields of Research (FOR2008): 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
URI: http://eprints.usq.edu.au/id/eprint/7209

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