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Extension of Meshless Galerkin/Petrov-Galerkin Approach without Using Lagrange Multipliers

Atsushi KAMITANI, Teruou TAKAYAMA, Taku ITOH¹⁾ and Hiroaki NAKAMURA²⁾

Yamagata University, Yonezawa 992-8510, Japan

1)

Seikei University, Musashino 180-8633, Japan

2)

National Institute for Fusion Science, Toki 509-5292, Japan

(Received 5 December 2010 / Accepted 19 April 2011 / Published 1 July 2011)

Abstract

By directly discretizing the weak form used in the finite element method, meshless methods have been derived. Neither the Lagrange multiplier method nor the penalty method is employed in the derivation of the methods. The resulting methods are divided into two groups, depending on whether the discretization is based on the Galerkin or the Petrov-Galerkin approach. Each group is further subdivided into two groups, according to the method for imposing the essential boundary condition. Hence, four types of the meshless methods have been formulated. The accuracy of these methods is illustrated for two-dimensional Poisson problems.

Copyright (c) 2011 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

boundary-value problem, collocation, essential boundary condition, Lagrange multiplier, meshless method, weak form

DOI: 10.1585/pfr.6.2401074

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References

• [1] B. Nayroles, G. Touzot and P. Villon, Comput. Mech. 10, 307 (1992).
• [2] T. Belytschko, Y.Y. Lu and L. Gu, Int. J. Numer. Meth. Engng. 37, 229 (1994).
• [3] S.N. Atluri and T. Zhu, Comput. Mech. 22, 117 (1998).
• [4] Y.X. Mukherjee and S. Mukherjee, Int. J. Numer. Meth. Engng. 40, 797 (1997).
• [5] M.K. Chati, G.H. Paulino and S. Mukherjee, Int. J. Numer. Meth. Engng. 50, 2233 (2001).
• [6] S. Ikuno, K. Takakura and A. Kamitani, IEEE Trans. Magn. 43, 1501 (2007).

This paper may be cited as follows:

Atsushi KAMITANI, Teruou TAKAYAMA, Taku ITOH and Hiroaki NAKAMURA, Plasma Fusion Res. 6, 2401074 (2011).