A multidomain integrated RBF collocation method for elliptic differential equations

Mai-Duy, Nam and Tran-Cong, Thanh (2008) A multidomain integrated RBF collocation method for elliptic differential equations. In: 8th World Congress on Computational Mechanics (WCCM8), and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), 30 June - 4 July 2008, Venice, Italy.

Abstract

[Abstract]: This paper describes a non-overlapping multidomain radial-basis-function (RBF) technique that improves smoothness of the approximate solution across subdomain interfaces. In general, the procedure is similar to the Schur complement approach where the interface solutions are obtained before the subdomain solutions. In particular, subdomain problems are solved using the integrated RBF collocation technique. On each subdomain, highest-order derivatives in the given differential equation (DE) are approximated using RBF networks, and lower-order derivatives and the variable itself are then obtained through integration. The present integrated RBF technique introduces integration constants which provide an effective means to collocate the DE on the interfaces. Continuity enforcements employed in the Schur complement system and the satisfaction of the DE on the subdomain interfaces in the subdomain discrete system leads to a solution that is continuous across the interfaces with one order higher than with conventional domain decomposition techniques.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: Awaiting copyright advice.
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 22 May 2009 03:45
Last Modified: 09 Dec 2014 06:01
Uncontrolled Keywords: RBF, integral collocation formulation, domain decomposition
Fields of Research (FOR2008): 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
URI: http://eprints.usq.edu.au/id/eprint/4576

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