A meshless IRBFN-based method for transient problems

Mai-Cao, L. and Tran-Cong, T. (2005) A meshless IRBFN-based method for transient problems. CMES: Computer Modeling in Engineering and Sciences, 7 (2). pp. 149-171. ISSN 1526-1492


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[Abstract]: The Indirect Radial Basis Function Network (IRBFN) method has been reported to be a highly accurate tool for approximating multivariate functions and solving elliptic partial differential equations (PDEs). The present method is a truly meshless method as defined in [\citet *{Atluri_Shen_02a}]. A recent development of the method for solving transient problems is presented in this paper. Two numerical schemes combining the IRBFN method with different time integration techniques based on either fully or semi-discrete framework are proposed. The two schemes are implemented making use of Hardy's multiquadrics (MQ) and Duchon's thin plate splines (TPS). Some example problems are solved by the present method, and the results compare favorably in terms of accuracy and efficiency with those from other numerical methods such as finite difference (FDM), finite element (FEM), boundary element (BEM) and the Direct Radial Basis Function Network (DRBFN) methods.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Awaiting copyright advice.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 11 Oct 2007 01:18
Last Modified: 02 Jul 2013 22:48
Uncontrolled Keywords: meshless method; radial basis functions; IRBFN method; time-dependent PDEs
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
URI: http://eprints.usq.edu.au/id/eprint/2984

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