A Cartesian-grid integrated-RBF Galerkin technique

Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A Cartesian-grid integrated-RBF Galerkin technique. In: Recent studies in meshless and other novel computational methods. Tech Science Press, Duluth, GA. USA, pp. 87-102. ISBN 0-9824205-4-4

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Abstract

This paper describes a high-order Galerkin technique, which is based on indirect/integrated radial-basis-function networks (IRBFNs) and Cartesian grids, for the discretisation of elliptic problems in two dimensions. The field variable is approximated by high-order IRBFNs that can work on uniform grids without suffering from Runge’s phenomenon. Unlike conventional Galerkin techniques, derivative boundary values are incorporated into the approximations and their imposition is conducted in an exact manner. The Galerkin formulation is then applied to force IRBFNs to satisfy the governing equation. The present technique is verified numerically through the solution natural convection in a square slot - a benchmark problem in CFD. Highly accurate solutions are obtained using relatively coarse grids, which show the effectiveness of using RBFs as trial functions in the Galerkin formulation.


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Item Type: Book Chapter (Commonwealth Reporting Category B)
Refereed: Yes
Item Status: Live Archive
Additional Information: Chapter 6. © 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 05:21
Last Modified: 03 Oct 2014 03:13
Uncontrolled Keywords: integrated RBFNs; Galerkin approach; Cartesian grids; elliptic 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/18256

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