A meshless technique based on integrated radial basis function networks for elliptic partial differential equations

Mai-Duy, N. and Tran-Cong, T. (2008) A meshless technique based on integrated radial basis function networks for elliptic partial differential equations. In: 4th International Workshop on Meshfree Methods for Partial Differential Equations, 17-20 Sep 2007, Bonn, Germany.

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Abstract

This paper presents a meshless technique based on radial basis function networks (RBFNs) for solving Dirichlet boundary value problems governed by the Poisson and biharmonic equations. The technique employs integrated RBFNs (IRBFNs) to approximate the field variable and point collocation to discretize the PDE. The boundary conditions are incorporated into IRBFNs via integration constants, which occurs prior to the transformation of the network-weight spaces into the physical space. Several linear and nonlinear test problems are considered to demonstrate the attractiveness of the present meshless technique.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: Copyright Springer. This is the author's version of a paper published in the series Lecture Notes in Computational Science and Engineering. Author's version deposited with blanket permssion of publisher, Springer. Print copy held in USQ Library at call no. 515.353 Mes.
Depositing User: Prof Thanh Tran-Cong
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 26 May 2009 04:06
Last Modified: 02 Jul 2013 23:09
Uncontrolled Keywords: radial basis functions; meshless discretization; integral collocation formulation
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1007/978-3-540-79994-8_9
URI: http://eprints.usq.edu.au/id/eprint/4599

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