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

Authors:
N. Mai-Duy;T. Tran-Cong
Affiliations:
Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, University of Southern Queensland, Toowoomba, QLD 4350, Australia;Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, University of Southern Queensland, Toowoomba, QLD 4350, Australia
Venue:
Journal of Computational Physics
Year:
2011

Citing 4
Cited 1

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A compact five-point stencil based on integrated RBFs for 2D second-order differential problems

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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.