A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations

Mai-Duy, Nam and Ho-Minh, D. and Tran-Cong, Thanh (2009) A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations. International Journal of Computer Mathematics, 86 (10-11). pp. 1746-1759. ISSN 0020-7160

Abstract

This paper is concerned with the use of integrated radial basis function networks (IRBFNs) for the discretisation of Galerkin approximations for Dirichlet biharmonic problems in two dimensions. The field variable is approximated by global high-order IRBFNs on uniform grids without suffering from Runge's phenomenon. Double boundary conditions, which can be of complicated shapes, are both satisfied identically. The proposed technique is verified through the solution of linear and nonlinear problems, including a benchmark buoyancy-driven flow in a square slot. Good accuracy and fast convergence are obtained.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to paper due to publisher copyright restrictions. Originally a paper from 8th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE-2008) 'Solving 2D biharmonic equations by the Galerkin approach using integrated radial basis function networks'.
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 08 Jan 2010 12:13
Last Modified: 11 Nov 2014 00:11
Uncontrolled Keywords: Galerkin formulation; integrated RBFs; biharmonic equations; double boundary conditions
Fields of Research (FOR2008): 01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
01 Mathematical Sciences > 0101 Pure Mathematics > 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: doi: 10.1080/00207160802647365
URI: http://eprints.usq.edu.au/id/eprint/6492

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