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Mathematical Problems in Engineering
Volume 2014, Article ID 323945, 13 pages
Research Article

An Improved Interpolating Element-Free Galerkin Method Based on Nonsingular Weight Functions

1Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
2Faculty of Science, Ningbo University of Technology, Ningbo 315016, China

Received 23 December 2013; Accepted 21 January 2014; Published 2 March 2014

Academic Editor: Miaojuan Peng

Copyright © 2014 F. X. Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based on the moving least-squares (MLS) approximation, an improved interpolating moving least-squares (IIMLS) method based on nonsingular weight functions is presented in this paper. Then combining the IIMLS method and the Galerkin weak form, an improved interpolating element-free Galerkin (IIEFG) method is presented for two-dimensional potential problems. In the IIMLS method, the shape function of the IIMLS method satisfies the property of Kronecker function, and there is no difficulty caused by singularity of the weight function. Then in the IIEFG method presented in this paper, the essential boundary conditions are applied naturally and directly. Moreover, the number of unknown coefficients in the trial function of the IIMLS method is less than that of the MLS approximation; then under the same node distribution, the IIEFG method has higher computational precision than element-free Galerkin (EFG) method and interpolating element-free Galerkin (IEFG) method. Four selected numerical examples are presented to show the advantages of the IIMLS and IIEFG methods.