# 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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Le_Rabczuk_Mai-Duy_Tran-Cong_CMES_2010_AV.pdf

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.