single-jc.php

JACIII Vol.16 No.4 pp. 496-502
doi: 10.20965/jaciii.2012.p0496
(2012)

Paper:

A Large-Scale Magnetostatic Analysis Using an Iterative Domain Decomposition Method Based on the Minimal Residual Method

Masao Ogino*, Shin-ichiro Sugimoto**, Seigo Terada***,
Yanqing Bao***, and Hiroshi Kanayama***

*Information Technology Center, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan

**Department of Systems Innovation, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

***Department of Mechanical Engineering, Graduate School of Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

Received:
December 11, 2011
Accepted:
March 25, 2012
Published:
June 20, 2012
Keywords:
minimal residual method, conjugate residual method, domain decomposition method, finite element method, large-scale magnetostatic problems
Abstract
This paper describes a large-scale 3D magnetostatic analysis using the Domain Decomposition Method (DDM). To improve the convergence of the interface problem of DDM, a DDM approach based on the Conjugate Residual (CR) method or the MINimal RESidual (MINRES) method is proposed. The CR or MINRES method improved the convergence rate and showed more stable convergence behavior in solving the interface problem than the Conjugate Gradient (CG) method, and reduced computation time for a large-scale problem with about 10 million degrees of freedom.
Cite this article as:
M. Ogino, S. Sugimoto, S. Terada, Y. Bao, and H. Kanayama, “A Large-Scale Magnetostatic Analysis Using an Iterative Domain Decomposition Method Based on the Minimal Residual Method,” J. Adv. Comput. Intell. Intell. Inform., Vol.16 No.4, pp. 496-502, 2012.
Data files:
References
  1. [1] A. Quarteroni and A. Vali, “Domain Decomposition Methods for Partial Differential Eequations,” Clarendon Press Oxford, 1999.
  2. [2] R. Shioya and G. Yagawa, “Iterative domain decomposition FEM with preconditioning technique for large scale problem,” ECM’99 Progress in Experimental and Computational Mechanics in Engineering and Material Behaviour, pp. 255-260, 1999.
  3. [3] A. M. M. Mukaddes, M. Ogino, H. Kanayama, and R. Shioya, “A scalable balancing domain decomposition based preconditioner for large scale heat transfer problems,” JSME Int. J. Series B, Vol.49, No.2, pp. 533-540, 2006.
  4. [4] B. Faucard, A. G. Sorguç, F. Magoulès, and I. Hagiwara, “Refining technique for multilevel graph k-partitioning and its application on domain decomposition non overlapping Schwarz technique for urban acoustic pollution,” Trans. of JSST, Vol.1, No.2, pp. 17-27, 2009.
  5. [5] H. Kanayama and S. Sugimoto, “Effectiveness of A-phi method in a parallel computing with an iterative domain decomposition method,” IEEE Trans. on Magnetics, Vol.42, No.4, pp. 539-542, 2006.
  6. [6] H. Kanayama, H. Zheng, and N. Maeno, “A domain decomposition method for large-scale 3-D nonlinear magnetostatic problems,” Theoretical and Applied Mechanics, Vol.52, pp. 247-254, 2003.
  7. [7] H. Kanayama, R. Shioya, D. Tagami, and H. Zheng, “A numerical procedure for 3-D nonlinear magnetostatic problems using the magnetic vector potential,” Theoretical and Applied Mechanics, Vol.50, pp. 411-418, 2001.
  8. [8] H. Kanayama, M. Ogino, S. Sugimoto, and J. Zhao, “Non-linear magnetostatic analysis of a 100 million DOF problem with hierarchical domain decomposition method,” Trans. of the Japan Society for Simulation Technology, Vol.2, No.1, pp. 1-8, 2009. (in Japanese)
  9. [9] E. F. Kaasschieter, “Preconditioned conjugate gradients for solving singular systems,” J. of Computational and Applied Mathematics, Vol.24, No.1-2, pp. 265-275, 1988.
  10. [10] H. A. Van der Vorst, “Iterative Krylov Methods for Large Linear Systems,” Cambridge University Press, 2003.
  11. [11] M. Mori, M. Sugihara, and K. Murota, “Linear Computation,” Iwanami Shoten, 1994. (in Japanese)
  12. [12] A. Greenbaum, “Iterative Methods for Solving Linear Systems,” SIAM, Philadelphia, 1997.
  13. [13] M. R. Hestenes and E. Stiefel, “Methods of conjugate gradients for solving linear systems,” J. of Research of the National Bureau of Standards, Vol.49, pp. 409-436, 1952.
  14. [14] E. Stiefel, “Relaxationsmethoden bester strategie zur lösung linearer gleichungssysteme,” Commentarii Mathematici Helvetici, Vol.29, pp. 157-179, 1955.
  15. [15] C. C. Paige and M. A. Saunders, “Solution of sparse indefinite systems of linear equations,” SIAM J. Numer. Anal, Vol.12, No.4, pp. 617-629, 1975.
  16. [16] IEEJ, “IEEJ Technical Report No.486,” IEEJ, 1994. (in Japanese)

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Oct. 01, 2024