# A moving IRBFN-based Galerkin meshless method

Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh (2010) A moving IRBFN-based Galerkin meshless method. CMES: Computer Modeling in Engineering and Sciences, 66 (1). pp. 25-52. ISSN 1526-1492

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## Abstract

A novel meshless method based on Radial Basis Function networks (RBFN) and variational principle (global weak form) is presented in this paper. In this method, the global integrated RBFN is localized and coupled with the moving least square method via the partition of unity concept. As a result, the system matrix is symmetric, sparse and banded. The trial and test functions satisfy the Kronecker-delta property, i.e. $\Phi_i(\mathbf{x}_j)=\delta_{ij}$. Therefore, the essential boundary conditions are imposed in strong form as in the FEMs. Moreover, the proposed method is applicable to scattered nodes and arbitrary domains. The method is examined with several numerical examples and the results indicate that the accuracy and the rate of convergence of the proposed method are superior to those of the EFG method using linear basis functions. In addition, the method does not exhibit any volumetric locking near the limit of incompressible material.

Item Type: Article (Commonwealth Reporting Category C) Yes Live Archive Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering 10 Mar 2011 11:14 10 Oct 2014 05:20 RBF; local IRBF; moving IRBF; partition of unity; meshless; elasticity; crack; superconvergence 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation09 Engineering > 0915 Interdisciplinary Engineering > 091502 Computational Heat Transfer E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in EngineeringE Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences doi: 10.3970/cmes.2010.066.025 http://eprints.usq.edu.au/id/eprint/18294

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