An integrated-RBF technique based on Galerkin formulation for elliptic differential equations

Mai-Duy, Nam and Tran-Cong, Thanh (2009) An integrated-RBF technique based on Galerkin formulation for elliptic differential equations. Engineering Analysis with Boundary Elements, 33 (2). pp. 191-199. ISSN 0955-7997

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This paper presents a new radial-basis-function (RBF) technique for solving elliptic differential equations (DEs). The RBF solutions are sought to satisfy (a) the boundary conditions in a local sense using the point-collocation formulation, (b) the governing equation in a global sense using the Galerkin formulation. In contrast to Galerkin finite-element techniques, the present Neumann boundary conditions are imposed in an exact manner. Unlike conventional RBF techniques, the present RBF approximations are constructed 'locally' on grid lines through integration and they are expressed in terms of nodal variable values. The proposed technique can provide an approximate solution that is a Cp function across the subdomain interfaces (p—the order of the DE). Several numerical examples are presented to demonstrate the attractiveness of the present implementation.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Accepted Version deposited in accordance with the copyright policy of the publisher (Elsevier).
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 10 Jan 2010 02:35
Last Modified: 02 Jul 2013 23:34
Uncontrolled Keywords: integrated RBFNs; Galerkin formulation; Neumann boundary conditions; multiple boundary conditions; domain decomposition
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: 10.1016/j.enganabound.2008.05.001

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