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New Implementation Method for Essential Boundary Condition to Extended Element-Free Galerkin Method: Application to Nonlinear Problem

Ayumu SAITOH, Taku ITOH¹⁾, Nobuyuki MATSUI, Atsushi KAMITANI²⁾ and Hiroaki NAKAMURA³⁾

University of Hyogo, Himeji 671-2280, Japan

1)

Seikei University, 3-3-1, Kichijoji-Kitamachi, Musashino 180-8633, Japan

2)

Yamagata University, 4-3-16, Johnan, Yonezawa 992-8510, Japan

3)

National Institute for Fusion Science, 322-6, Oroshi-cho, Toki 509-5292, Japan

(Received 22 December 2010 / Accepted 22 April 2011 / Published 12 July 2011)

Abstract

A new method has been proposed for implementing essential boundary conditions to the Element-Free Galerkin Method (EFGM) without using the Lagrange multiplier. Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that, as interpolation functions become closer to delta functions, the accuracy of the solution is improved on the boundary. In addition, the accuracy of the proposed method is higher than that of the conventional EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem.

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

Keywords

finite element method, element-free Galerkin method, Lagrange multiplier, nonlinear problem

DOI: 10.1585/pfr.6.2401089

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References

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This paper may be cited as follows:

Ayumu SAITOH, Taku ITOH, Nobuyuki MATSUI, Atsushi KAMITANI and Hiroaki NAKAMURA, Plasma Fusion Res. 6, 2401089 (2011).