A numerical scheme based on local integrated RBFNs and Cartesian grids for solving second-order elliptic problems in two dimensions

Mai-Duy, N. and Tran-Cong, T. (2010) A numerical scheme based on local integrated RBFNs and Cartesian grids for solving second-order elliptic problems in two dimensions. In: Recent studies in meshless and other novel computational methods. Tech Science Press, Duluth, GA. United States, pp. 17-33. ISBN 978-0-9824205-4-6

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Abstract

This paper reports a new Cartesian-grid computational technique, based on local integrated radial-basis-function networks (IRBFNs), for the solution of second-order elliptic differential problems defined on two-dimensional regular and irregular domains. At each grid point, only neighbouring nodes are activated to construct the IRBFN approximations. Local IRBFNs are introduced into two different schemes for discretisation of partial differential equations, namely point collocation and control-volume (CV)/subregion-collocation. Numerical experiments indicate that the latter outperforms the former regarding accuracy. Moreover, the proposed local IRBFN CV method shows a similar level of the matrix condition number and a significant improvement in accuracy over a linear CV method.

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Item Type:	Book Chapter (Commonwealth Reporting Category B)
Refereed:	Yes
Item Status:	Live Archive
Additional Information:	© Tech Science Press 2010. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher.
Faculty/School / Institute/Centre:	Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Faculty/School / Institute/Centre:	Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Date Deposited:	18 Mar 2011 05:31
Last Modified:	05 Sep 2016 03:22
Uncontrolled Keywords:	local approximations; integrated RBFNs; point collocation; subregion collocation; second-order differential problems
Fields of Research (2008):	01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations 01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods 09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Fields of Research (2020):	49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490410 Partial differential equations 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490101 Approximation theory and asymptotic methods 40 ENGINEERING > 4017 Mechanical engineering > 401706 Numerical modelling and mechanical characterisation
Socio-Economic Objectives (2008):	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/18255

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