RBF computation of multiscale elliptic problems [Keynote paper]

An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) RBF computation of multiscale elliptic problems [Keynote paper]. In: 8th ICCES Special Symposium on Meshless & Other Novel Computational Methods (ICCES MM 2012), 2-6 Sep 2012, Budva, Montenegro.

Abstract

Many important engineering problems have multiple-scale solutions. Composites materials, 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 highly accurate IRBF formulations. High accuracy and efficiency of this method are demonstrated by several one- and two-dimensional
examples.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Lecture)
Refereed: No
Item Status: Live Archive
Additional Information: Copyright 2012 University of Montenegro Press.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 28 May 2013 02:12
Last Modified: 01 Feb 2017 01:23
Uncontrolled Keywords: multiscale elliptic problem
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
08 Information and Computing Sciences > 0801 Artificial Intelligence and Image Processing > 080110 Simulation and Modelling
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
URI: http://eprints.usq.edu.au/id/eprint/23078

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