Plasma and Fusion Research

Volume 11, 2406021 (2016)

Regular Articles

Krylov Subspace Method with Communication Avoiding Technique for Linear System Obtained from Electromagnetic Analysis
Soichiro IKUNO, Gong CHEN, Susumu YAMAMOTO, Taku ITOH1), Kuniyoshi ABE2) and Hiroaki NAKAMURA3,4)
School of Computer Science, Tokyo University of Technology, Tokyo 192-0982, Japan
College of Industrial Technology, Nihon University, Narashino 275-8575, Japan
Faculty of Economics and Information, Gifu Shotoku Gakuen University, Gifu 500-8288, Japan
Department of Energy Engineering and Science, Nagoya University, Toki 509-5292, Japan
National Institute for Fusion Science, Toki 509-5292, Japan
(Received 9 December 2015 / Accepted 20 January 2016 / Published 17 March 2016)


Krylov subspace method and the variable preconditioned Krylov subspace method with communication avoiding technique for a linear system obtained from electromagnetic analysis are numerically investigated. In the k-skip Krylov method, the inner product calculations are expanded by Krylov basis, and the inner product calculations are transformed to the scholar operations. k-skip CG method is applied for the inner-loop solver of Variable Preconditioned Krylov subspace methods, and the converged solution of electromagnetic problem is obtained using the method.


Krylov subspace method, communication avoiding technique, electromagnetic analysis, prallelization, GPGPU

DOI: 10.1585/pfr.11.2406021


  • [1] Y. Saad, SIAM J. Sci. Stat. Comput. 6(4), 865 (1985).
  • [2] G. Meurant, Parallel Comput. 5(3), 267 (1987).
  • [3] M. Hoemmen, The doctoral dissertation of University of California at Berkeley, Berkeley, CA, USA, 2010.
  • [4] T. Motoya and R. Suda, IPSJ SIG Tech. Rep., Vol.2012-HPC-133, No.30 (2012) (Japanese).
  • [5] E.F. D'Azevedo, V. Eijkhout and C.H. Romine, Technical Report, Mathematical Sciences Section, Oak Ridge National Laboratory, 1999.
  • [6] A.T. Chronopoulos and C.W. Gear, J. Comput. Appl. Math. 25(2), 153 (1989).
  • [7] K. Abe and S.L. Zhang, Int. J. Numer. Anal. Model. 2, No.2, 137 (2005).
  • [8] S. Ikuno, Y. Kawaguchi, T. Itoh, S. Nakata and K. Watanabe, IEEE Trans. Magn. 48, No.2, 467 (2012).
  • [9]