Regular Articles

Full Text / References

Application of Collocation Meshless Method to Eigenvalue Problem

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

University of Hyogo, Himeji, Hyogo 671-2280, Japan

1)

Seikei University, Musashino, Tokyo 180-8633, Japan

2)

Yamagata University, Yonezawa, Yamagata 992-8510, Japan

3)

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

(Received 9 December 2011 / Accepted 18 May 2012 / Published 26 July 2012)

Abstract

The numerical method for solving the nonlinear eigenvalue problem has been developed by using the collocation Element-Free Galerkin Method (EFGM) and its performance has been numerically investigated. The results of computations show that the approximate solution of the nonlinear eigenvalue problem can be obtained stably by using the developed method. Therefore, it can be concluded that the developed method is useful for solving the nonlinear eigenvalue problem.

Copyright (c) 2012 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

element-free Galerkin method, finite element method, nonlinear eigenvalue problem, Grad-Shafranov equation, numerical analysis

DOI: 10.1585/pfr.7.2406096

Full Text

PDF format (776Kbytes)

References

• [1] S. Ikuno, A. Kamitani and M. Natori, J. JSAEM 6(1), 63 (1998) [in Japanese].
• [2] M. Itagaki and T. Fukunaga, Eng. Anal. Boundary Elements 30, 746 (2006).
• [3] T. Belytchko, Y.Y. Lu and L. Gu, Int. J. Numer. Methods Eng. 37, 229 (1994).
• [4] S.N. Atluri and T. Zhu, Comput. Mech. 22(2), 117 (1998).
• [5] A. Kamitani, T. Takayama, T. Itoh and H. Nakamura, Plasma Fusion Res. 6, 2401074 (2011).
• [6] A. Saitoh, T. Itoh, N. Matsui and A. Kamitani, IEEE Trans. Magn. 48(2), 487 (2012).
• [7] J. Meijerink and H.A. van der Vorst, Math. Comput. 31, 148 (1977).

This paper may be cited as follows:

Ayumu SAITOH, Taku ITOH, Nobuyuki MATSUI, Atsushi KAMITANI and Hiroaki NAKAMURA, Plasma Fusion Res. 7, 2406096 (2012).