RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients

An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients. CMES: Computer Modeling in Engineering and Sciences, 89 (4). pp. 303-359. ISSN 1526-1492

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Many important engineering problems have multiple-scale solutions. Thermal conductivity of composite materials, flow in porous media, and turbulent transport in high Reynolds number flows are examples of this type. Direct numerical simulations for these problems typically
require extremely large amounts of CPU time and computer memory, which may be too expensive or impossible on the present supercomputers. In this paper, we develop a high order computational method, based on multiscale basis function approach and integrated radial-basis-function (IRBF) approximant, for the solution of multiscale elliptic problems with reduced computational cost. Unlike other methods based on multiscale basis function approach, sets of basis and correction functions here are obtained through $C^2$-continuous IRBF element formulations. High accuracy and efficiency of this method are demonstrated by several one- and two-dimensional examples.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Copyright © 2012 Tech Science Press. Permanent restricted access to Published Version of paper due to publisher copyright policy.
Faculty/School / Institute/Centre: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 18 Mar 2013 12:37
Last Modified: 22 Aug 2014 06:31
Uncontrolled Keywords: integrated radial basis functions; multiscale elliptic problems; Cartesian grid; control volume method; multiscale method
Fields of Research : 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
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.3970/cmes.2012.089.303
URI: http://eprints.usq.edu.au/id/eprint/23174

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