Abstract
An iterative procedure using finite element method without the Lagrange multiplier is proposed for three-dimensional eddy current problems, which is based on an iterative procedure derived from a perturbation problem of the magnetostatic problem. To consider the continuity of an excitation current density, a correction method is also proposed. Numerical results show that the BiConjugate Gradient (BiCG) method is applicable to the complex symmetric linear systems arising in the iterative procedure, and that approximate physical quantities are suitable.
Similar content being viewed by others
References
A. Alonso and A. Valli, A domain decomposition approach for heterogeneous time-harmonic Maxwell equations. Comput. Methods Appl. Mech. Engrg.,143 (1997), 97–112.
A. Bossavit, Computational Electromagnetism. Academic Press, 1998.
R.W. Freund, Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices. SIAM J. Sci. Stat. Comput.,13 (1992), 425–448.
K. Pujiwara and T. Nakata, Results for benchmark problem 7 (asymmetrical conductor with a hole). COMPEL,9 (1990), 137–154.
K. Pujiwara, T. Nakata, N. Takahashi and H. Ohashi, On the continuity of the magnetizing current density in 3-D magnetic field analysis with edge element. IEEE Trans. Magnetics,31, No. 3 (1995), 1364–1367.
A. Kameari and K. Koganezawa, Convergence of ICCG method in FEM using edge elements without gauge condition. IEEE Trans. Magnetics,33, No. 2 (1997), 1223–1226.
H. Kanayama, S. Ikeguchi and F. Kikuchi, 3-D eddy current analysis using the Nedelec elements. Proc. of ICES ’97, 1997, 277–282.
H. Kanayama and F. Kikuchi, 3-D eddy current computation using the Nedelec elements. Information,2 (1999), 37–46.
H. Kanayama, D. Tagami, M. Saito and F. Kikuchi, A finite element analysis of 3-D eddy current problems using an iterative method. Trans. of JSCES, No.20000033 (2000); http://homer.shinshu-u.ac.jp/jsces/trans/trans2000/No20000033.pdf.
H. Kanayama, D. Tagami, M. Saito, T. Take and S. Asakawa, A finite element method for 3-D eddy current problems using an iterative approach. To appear in Int. J. Comput. Fluid Dyn.
F. Kikuchi, Mixed formulations for finite element analysis of magnetostatic and electrostatic problems. Japan J. Appl. Math.,6 (1989), 209–221.
F. Kikuchi, On a discrete compactness property for the Nedelec finite elements. J. Fac. Sci. Univ. Tokyo, Sect. IA Math.,36 (1989), 479–490.
F. Kikuchi and M. Fukuhara, An iteration method for finite element analysis of magnetostatic problems. Lecture Notes in Numer. Appl. Anal.14, 1995, 93–105.
T.A. Manteuffel, An incomplete factorization technique for positive definite linear systems. Math. Comp.,34 (1980), 473–497.
J.C. Nedelec, Mixed finite element in ℝ3. Numer. Math.,35 (1980), 315–341.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Kanayama, H., Tagami, D., Saito, M. et al. A numerical method for 3-D eddy current problems. Japan J. Indust. Appl. Math. 18, 603–612 (2001). https://doi.org/10.1007/BF03168593
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF03168593