中国物理B ›› 2012, Vol. 21 ›› Issue (9): 90203-090203.doi: 10.1088/1674-1056/21/9/090203

• GENERAL • 上一篇    下一篇

A new complex variable element-free Galerkin method for two-dimensional potential problems

程玉民, 王健菲, 白福浓   

  1. a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
    b Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
  • 收稿日期:2011-12-23 修回日期:2012-02-23 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), the Shanghai Leading Academic Discipline Project, China (Grant No. S30106), and the Innovation Fund Project for Graduate Student of Shanghai University, China (Grant No. SHUCX112359).

A new complex variable element-free Galerkin method for two-dimensional potential problems

Cheng Yu-Min (程玉民), Wang Jian-Fei (王健菲), Bai Fu-Nong (白福浓)   

  1. a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
    b Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
  • Received:2011-12-23 Revised:2012-02-23 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), the Shanghai Leading Academic Discipline Project, China (Grant No. S30106), and the Innovation Fund Project for Graduate Student of Shanghai University, China (Grant No. SHUCX112359).

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摘要： In this paper, based on the element-free Galerkin (EFG) method and the improved complex variable moving least-square (ICVMLS) approximation, a new meshless method, which is the improved complex variable element-free Galerkin (ICVEFG) method, for two-dimensional potential problems is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square (CVMLS) approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.

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

Abstract: In this paper, based on the element-free Galerkin (EFG) method and the improved complex variable moving least-square (ICVMLS) approximation, a new meshless method, which is the improved complex variable element-free Galerkin (ICVEFG) method, for two-dimensional potential problems is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square (CVMLS) approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.

Key words: meshless method, improved complex variable moving least-square approximation, improved complex variable 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)