Plasma and Fusion Research

Volume 18, 2403039 (2023)

Regular Articles

Improved Variable-Reduction Method and Its Variant for Solving Asymmetric EFG-Type Saddle-Point Problem
Atsushi KAMITANI, Yuito SHINDO, Teruou TAKAYAMA and Hiroaki NAKAMURA1,2)
Yamagata University, Yonezawa, Yamagata 992-8510, Japan
1)
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan
2)
Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan
(Received 13 December 2022 / Accepted 10 April 2023 / Published 12 May 2023)

Abstract

If a boundary-value problem is discretized with the extended Element-Free Galerkin (EFG) method, an asymmetric EFG-type Saddle-Point (EFG-SP) problem is obtained. Although the improved Variable-Reduction Method (iVRM) was originally developed as a solver for symmetric EFG-SP problems, it is extended so as to be applicable to asymmetric EFG-SP problems. As a result, not only the Asymmetric-version iVRM (AiVRM) but also its variant AiVRM2 is developed. A numerical code is developed for solving an asymmetric EFG-SP problem with the AiVRM/AiVRM2 and, by means of the code, performances of the two methods are investigated numerically. Consequently, it is found that, especially for a large-scale asymmetric EFG-SP problem, both the AiVRM and the AiVRM2 are more effective than the preconditioned Krylov subspace method.

Keywords

computer simulation, element-free Galerkin method, Krylov subspace method, meshless approach, preconditioning, saddle-point problem

DOI: 10.1585/pfr.18.2403039

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References

  • [1] T. Belytschko, Y.Y. Lu and L. Gu, Int. J. Numer. Meth. Eng. 37, 229 (1994).
  • [2] A. Kamitani, T. Takayama, T. Itoh and H. Nakamura, Plasma Fusion Res. 6, 2401074 (2011).
  • [3] A. Kamitani, T. Takayama, A. Saitoh and H. Nakamura, Plasma Fusion Res. 17, 2403014 (2022).
  • [4] M. Rozložník, Saddle-Point Problems and Their Iterative Solution (Birkhäuser, Switzerland, 2018) Chaps. 1 and 4.
  • [5] M. Benzi, G.H. Golub and J. Liesen, Acta Numer. 14, 1 (2005).
  • [6] G.H. Golub and C.F. Van Loan, Matrix Computations, 4th ed. (Johns Hopkins University Press, Maryland, 2013) p.246.
  • [7] W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in Fortran 77, 2nd ed. (Cambridge Univ. Press, New York, 1992) p. 708.
  • [8] T. Itoh, A. Saitoh, S. Ikuno and A. Kamitani, J. Adv. Simulat. Sci. Eng. 3, 188 (2017).