New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils

Mai-Duy, Nam and Strunin, Dmitry (2021) New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils. Engineering Analysis with Boundary Elements, 125. pp. 12-22. ISSN 0955-7997

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Abstract

This paper presents some new compact approximation stencils based on integrated radial basis functions (IRBFs) for numerically solving second-order elliptic differential problems on Cartesian grids. Higher-order IRBF schemes are employed to approximate the field/dependent variable. The IRBF approximations in each direction are based on 3 points and constructed independently, where derivatives of the second, third, fourth, fifth and sixth orders along the grid line are enforced at the two end-points. The imposed nodal derivative values are simply acquired through a Picard-type iteration scheme. The stencil is made up of 3 points and 5 points for 1D and 2D discretisations, respectively. Numerical results show that the proposed stencils yield a high rate of convergence with respect to grid refinement, e.g. up to the 13th order for 1D problems and to the 9th order for 2D problems.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Mechanical and Electrical Engineering (1 Jul 2013 - 31 Dec 2021)
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 - 31 Dec 2021)
Date Deposited: 09 Dec 2021 01:58
Last Modified: 13 Dec 2021 02:21
Uncontrolled Keywords: Compact approximation; Local approximation; Integrated radial basis function; 3-point stencil; 5-point stencil
Fields of Research (2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Fields of Research (2020): 40 ENGINEERING > 4017 Mechanical engineering > 401706 Numerical modelling and mechanical characterisation
49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490303 Numerical solution of differential and integral equations
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
Socio-Economic Objectives (2020): 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280110 Expanding knowledge in engineering
28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences
Identification Number or DOI: https://doi.org/10.1016/j.enganabound.2021.01.001
URI: http://eprints.usq.edu.au/id/eprint/44198

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