Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks

Mai-Duy, N. and Tran-Cong, T. (2006) Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks. Engineering Analysis With Boundary Elements, 30 (2). pp. 77-87. ISSN 0955-7997

Abstract

This paper reports a new indirect radial-basis-function (RBF) collocation method for numerically solving biharmonic boundary-value problems. The RBF approximations are constructed through an integration process. The new feature here is that integration constants are eliminated pointwise using the prescribed boundary conditions rather than employed as network weights. This treatment of integration constants is particularly well suited for the case of discretizing the governing differential equations on a set of scattered points. The proposed method is verified through the solution of benchmark test problems. Accurate results and high convergence rates are obtained.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright policy of the publisher.
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 11 Oct 2007 00:56
Last Modified: 02 Jul 2013 22:41
Uncontrolled Keywords: indirect radial-basis-function networks; point collocation; meshless method; biharmonic equations; multiple boundary conditions
Fields of Research (FOR2008): 08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080202 Applied Discrete Mathematics
01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
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
Identification Number or DOI: doi: 10.1016/j.enganabound.2005.10.004
URI: http://eprints.usq.edu.au/id/eprint/2078

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