中国物理B ›› 2012, Vol. 21 ›› Issue (9): 90204-090204.doi: 10.1088/1674-1056/21/9/090204

• GENERAL • 上一篇    下一篇

An improved interpolating element-free Galerkin method with nonsingular weight function for two-dimensional potential problems

王聚丰a b, 孙凤欣a c, 程玉民a   

  1. 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
  • 收稿日期:2012-02-20 修回日期:2012-03-04 出版日期:2012-08-01 发布日期:2012-08-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11171208) and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106).

An improved interpolating element-free Galerkin method with nonsingular weight function for two-dimensional potential problems

Wang Ju-Feng (王聚丰)a b, Sun Feng-Xin (孙凤欣)a c, Cheng Yu-Min (程玉民)a   

  1. 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
  • Received:2012-02-20 Revised:2012-03-04 Online:2012-08-01 Published:2012-08-01
  • Contact: Cheng Yu-Min E-mail:ymcheng@shu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11171208) and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106).

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摘要： 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.

关键词: meshless method, improved interpolating moving least-square method, improved interpolating element-free Galerkin method, potential problem

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.

Key words: meshless method, improved interpolating moving least-square method, improved interpolating element-free Galerkin method, potential problem

中图分类号:  (Numerical simulation; solution of equations)

  • 02.60.Cb
02.60.Lj (Ordinary and partial differential equations; boundary value problems) 02.30.Em (Potential theory)