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A Meshless IRBFN-based Method for Transient Problems

L. Mai-Cao1, T. Tran-Cong2
Faculty of Engineering and Surveying, University of Southern Queensland, Toowoomba Qld 4350, Australia.
Corresponding author, Faculty of Engineering and Surveying, University of Southern Queensland, Toowoomba Qld 4350, Australia, email: trancong@usq.edu.au, Fax: +61 7 46312526.

Computer Modeling in Engineering & Sciences 2005, 7(2), 149-172. https://doi.org/10.3970/cmes.2005.007.149

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.

Keywords

meshless method, radial basis functions, IRBFN method, time-dependent PDEs.

Cite This Article

Mai-Cao, L., Tran-Cong, T. (2005). A Meshless IRBFN-based Method for Transient Problems. CMES-Computer Modeling in Engineering & Sciences, 7(2), 149–172.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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