Open Access

ARTICLE

Indirect RBFN Method with Scattered Points for Numerical Solution of PDEs

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1 Corresponding author: Telephone +61 2 9351 7151, Fax +61 29351 7060, E-mail nam.maiduy@aeromech.usyd.edu.au, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia

Computer Modeling in Engineering & Sciences 2004, 6(2), 209-226. https://doi.org/10.3970/cmes.2004.006.209

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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