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
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan
Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan
(Received 13 December 2022 / Accepted 10 April 2023 / Published 12 May 2023)


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.


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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