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A Moving IRBFN-Based Galerkin Meshless Method

Phong B.H. Le1, Timon Rabczuk2, Nam Mai-Duy1, Thanh Tran-Cong1
CESRC, University of Southern Queensland, Toowoomba, QLD 4350, Australia.
Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstr. 15, 99423 Weimar, Germany.

Computer Modeling in Engineering & Sciences 2010, 66(1), 25-52.


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. Φi(xj) = δij. 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.


RBF, Local IRBF, Moving IRBF, partition of unity, meshless, elasticity, crack, superconvergence.

Cite This Article

Le, P. B., Rabczuk, T., Mai-Duy, N., Tran-Cong, T. (2010). A Moving IRBFN-Based Galerkin Meshless Method. CMES-Computer Modeling in Engineering & Sciences, 66(1), 25–52.

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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