Compact local integrated-RBF approximations for second-order elliptic differential problems

Mai-Duy, N. and Tran-Cong, T. (2011) Compact local integrated-RBF approximations for second-order elliptic differential problems. Journal of Computational Physics , 230 (12). pp. 4772-4794. ISSN 0021-9991

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Abstract

This paper presents a new compact approximation method for the discretisation of second-order elliptic equations in one and two dimensions. The problem domain, which can be rectangular or non-rectangular, is represented by a Cartesian grid. On stencils, which are three nodal points for one-dimensional problems and nine nodal points for two-dimensional problems, the approximations for the field variable and its derivatives are constructed using integrated radial basis functions (IRBFs). Several pieces of information about the governing differential equation on the stencil are incorporated into the IRBF approximations by means of the constants of integration. Numerical examples indicate that the proposed technique yields a very high rate of convergence with grid refinement.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to published version due to publisher copyright policy.
Depositing User: epEditor USQ
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - No Department
Date Deposited: 15 Sep 2011 04:07
Last Modified: 03 Jul 2013 00:46
Uncontrolled Keywords: compact local approximations; elliptic problems; high-order approximations; integrated radial basis functions
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
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.jcp.2011.03.002
URI: http://eprints.usq.edu.au/id/eprint/19637

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