A moving IRBFN-based integration-free meshless method

Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based integration-free meshless method. CMES: Computer Modeling in Engineering and Sciences, 61 (1). pp. 63-109. ISSN 1526-1492

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A novel approximation method using integrated radial basis function networks (IRBFN) coupled with moving least square (MLS) approximants, namely moving integrated radial basis function networks (MIRBFN), is proposed in this work. In this method, the computational domain w is divided into finite sub-domains w which satisfy point-wise overlap condition. The local function interpolation is constructed by using IRBFN supported by all nodes in subdomain w. The global function is then constructed by using Partition of Unity Method (PUM), where MLS functions play the role of partition of unity. As a result, the proposed method is locally supported and yields sparse and banded interpolation matrices. The computational efficiency are excellently improved in comparison with that of the original global IRBFN method. In addition, the present method possesses the Kronecker-d property, which makes it easy to impose the essential boundary conditions. The proposed method is applicable to randomly distributed datasets and arbitrary domains. In this work, the MIRBFN method is implemented in the collocation of a first-order system formulation to solve PDEs governing various problems including heat transfer, elasticity of both compressible and incompressible materials, and linear static crack problems. The numerical results show that the present method offers high order of convergence and accuracy.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Faculty/School / Institute/Centre: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 10 Mar 2011 11:40
Last Modified: 02 Apr 2015 04:09
Uncontrolled Keywords: RBF; local IRBF; moving IRBF; meshless; collocation method; elasticity; first order system; locking; crack
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
09 Engineering > 0915 Interdisciplinary Engineering > 091502 Computational Heat Transfer
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.2010.061.063
URI: http://eprints.usq.edu.au/id/eprint/18298

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