A Cartesian-grid integrated-RBF Galerkin technique

Ho-Minh, D. and Mai-Duy, N. and Tran-Cong, T. (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 978-0-9824205-4-6

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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:	© 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 05:21
Last Modified:	05 Sep 2016 03:16
Uncontrolled Keywords:	integrated RBFNs; Galerkin approach; Cartesian grids; elliptic problems
Fields of Research (2008):	01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations 08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080202 Applied Discrete Mathematics 08 Information and Computing Sciences > 0805 Distributed Computing > 080501 Distributed and Grid Systems
Fields of Research (2020):	49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490303 Numerical solution of differential and integral equations 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490199 Applied mathematics not elsewhere classified 46 INFORMATION AND COMPUTING SCIENCES > 4606 Distributed computing and systems software > 460605 Distributed systems and algorithms
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/18256

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