中国物理B ›› 2009, Vol. 18 ›› Issue (10): 4059-4064.doi: 10.1088/1674-1056/18/10/001

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Element-free Galerkin (EFG) method for a kind of two-dimensional linear hyperbolic equation

葛红霞1, 程荣军2, 程玉民3   

  1. (1)Faculty of Science, Ningbo University, Ningbo , China; (2)Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China; (3)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2009-02-12 修回日期:2009-04-08 出版日期:2009-10-20 发布日期:2009-10-20
  • 基金资助:
    Project supported by the Natural Science Foundation of Ningbo, China (Grant Nos 2009A610014, 2009A610154, 2008A610020 and 2007A610050).

Element-free Galerkin (EFG) method for a kind of two-dimensional linear hyperbolic equation

Cheng Rong-Jun(程荣军)a)† and Ge Hong-Xia(葛红霞)b)   

  1. a Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China; b Faculty of Science, Ningbo University, Ningbo , China
  • Received:2009-02-12 Revised:2009-04-08 Online:2009-10-20 Published:2009-10-20
  • Supported by:
    Project supported by the Natural Science Foundation of Ningbo, China (Grant Nos 2009A610014, 2009A610154, 2008A610020 and 2007A610050).

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摘要： The present paper deals with the numerical solution of a two-dimensional linear hyperbolic equation by using the element-free Galerkin (EFG) method which is based on the moving least-square approximation for the test and trial functions. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for hyperbolic problems needs only the scattered nodes instead of meshing the domain of the problem. It neither requires any element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for two-dimensional hyperbolic problems is investigated by two numerical examples in this paper.

Abstract: The present paper deals with the numerical solution of a two-dimensional linear hyperbolic equation by using the element-free Galerkin (EFG) method which is based on the moving least-square approximation for the test and trial functions. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for hyperbolic problems needs only the scattered nodes instead of meshing the domain of the problem. It neither requires any element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for two-dimensional hyperbolic problems is investigated by two numerical examples in this paper.

Key words: element-free Galerkin (EFG) method, meshless method, hyperbolic problem

中图分类号:  (Finite-element and Galerkin methods)

  • 02.70.Dh
02.30.Jr (Partial differential equations) 02.30.Sa (Functional analysis) 02.30.Xx (Calculus of variations) 02.60.Cb (Numerical simulation; solution of equations) 02.70.Rr (General statistical methods)