A symmetric integrated radial basis function method for solving differential equations

Mai-Duy, Nam and Dalal, Deepak and Le, Thi Thuy Van and Ngo-Cong, Duc and Tran-Cong, Thanh (2018) A symmetric integrated radial basis function method for solving differential equations. Numerical Methods for Partial Differential Equations, 34 (3). pp. 959-981. ISSN 0749-159X

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Abstract

In this article, integrated radial basis functions (IRBFs) are used for Hermite interpolation in the solution of differential equations, resulting in a new meshless symmetric RBF method. Both global and local approximation-based schemes are derived. For the latter, the focus is on the construction of compact approximation stencils, where a sparse system matrix and a high-order accuracy can be achieved together. Cartesian-grid-based stencils are possible for problems defined on nonrectangular domains. Furthermore, the effects of the RBF width on the solution accuracy for a given grid size are fully explored with a reasonable computational cost. The proposed schemes are numerically verified in some elliptic boundary-value problems governed by the Poisson and convection-diffusion equations. High levels of the solution accuracy are obtained using relatively coarse discretisations.


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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.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering
Date Deposited: 04 Feb 2019 02:47
Last Modified: 10 Jun 2019 03:07
Uncontrolled Keywords: compact local approximation, extended precision, flat radial basis function, global approximation, Hermite interpolation, integrated radial basis function
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010399 Numerical and Computational Mathematics not elsewhere classified
01 Mathematical Sciences > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified
Identification Number or DOI: 10.1002/num.22240
URI: http://eprints.usq.edu.au/id/eprint/35256

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