Chin. Phys. B, 2012, Vol. 21(9): 090204    DOI: 10.1088/1674-1056/21/9/090204
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# An improved interpolating element-free Galerkin method with nonsingular weight function for two-dimensional potential problems

Wang Ju-Fenga b, Sun Feng-Xina c, Cheng Yu-Mina
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
c Faculty of Science, Ningbo University of Technology, Ningbo 315016, China
Abstract  In this paper, an improved interpolating moving least-square (IIMLS) method is presented. The shape function of the IIMLS method satisfies the property of Kronecker δ function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. And the number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square (MLS) approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin (IIEFG) method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin (EFG) method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has a higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.
Keywords:  meshless method      improved interpolating moving least-square method      improved interpolating element-free Galerkin method      potential problem
Received:  20 February 2012      Revised:  04 March 2012      Accepted manuscript online:
 PACS: 02.60.Cb (Numerical simulation; solution of equations) 02.60.Lj (Ordinary and partial differential equations; boundary value problems) 02.30.Em (Potential theory)
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11171208) and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106).
Corresponding Authors:  Cheng Yu-Min     E-mail:  ymcheng@shu.edu.cn