Advertisement

Numerical Algorithms for the Calculation of Magneto-Quasistatic Fields Using the Finite Integration Technique

  • M. Clemens
  • S. Drobny
  • M. Wilke
  • T. Weiland
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 18)

Abstract

In this paper numerical algorithms for transient eddy current calculations based on the Finite Integration Technique are presented. The occuring differential-algebraic systems of equations, whose initial degeneration requires to deal with the problem of a suitable regularization, allows to successfully include nonlinear ferromagnetic material behavior using various linearization techniques as well as eddy current effects due to moving conductors. Techniques for error controlled adaptive time stepping and first results of a new algebraic multigrid solver for the linear systems of equations of the implicit time integration process are presented.

Keywords

Magnetic Head Eddy Current Test Implicit Time Integration Nonlinear Material Behavior Eddy Current Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arnold, D., Falk, R., Winther, R.: Multigrid in h(div) and in h(curl) (1999). Numer. Math., to appear.Google Scholar
  2. 2.
    Bossavit, A.: ’stiff’ problems in eddy-current theory and the regularization of Maxell’s equations. In Conference Records of the CEFC 2000, Milwaukee (1997) 497. Full paper submitted to IEEE Transactions on Magnetics.Google Scholar
  3. 3.
    Cameron, F., Piché, R., Forsman, K.: Variable step size time integration methods for transient eddy current problems. IEEE Transactions on Magnetics 34 (1998) 3319–3323CrossRefGoogle Scholar
  4. 4.
    Clemens, M., Drobny, S., Weiland, T.: Time integration of slowly-varying electromagnetic field problems using the finite integration technique. In Proceedings of the ENUMATH 97, Heidelberg (1999) 246–253Google Scholar
  5. 5.
    Clemens, M., Weiland, T.: Numerical algorithms for the FDiTD and FDFD simulation of slowly-varying electromagnetic fields. Int. J. Num. Mod. 12 (1999) 3–22zbMATHCrossRefGoogle Scholar
  6. 6.
    Transient eddy current calculation with the FI-method. IEEE Transactions on Magnetics 35 (1999) 1163–1166Google Scholar
  7. 7.
    Clemens, M., Weiland, T., Wilke, M.: Transient eddy current formulation including moving conductors using the finite integration method. In Honma, T., (ed.) Proceedings of the CEFC’99, Sapporo, Japan volume 2 (1999) 592–593Google Scholar
  8. 8.
    Drobny, S., Weiland, T.: Iterative algorithms for nonlinear transient electromagnetic field calculation (1999). Proceedings of the ISEM 99, Pavia, Italy.Google Scholar
  9. 9.
    Fujiwara, K., et al.: Thin film write head field analysis using a benchmark problem. In Proc. Compumag99 Conference, Sapporo (1999) 744–745Google Scholar
  10. 10.
    Gustafsson, K.: Control-theoretic techniques for stepsize selection in implicit runge-kutta methods. ACM Transactions on Mathematical Software 20 (1994) 496–517MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Hahne, P.: Zur Numerischen Berechnung Zeitharmonischer Elektromagnetischer Felder. Ph.D. thesis Technische Hochschule Darmstadt (1992)Google Scholar
  12. 12.
    Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems. Springer-Verlag, Wien, New York (1996)Google Scholar
  13. 13.
    Lang, J.: Two-dimensional fully adaptive solutions of reaction diffusion equations. Applied Numerical Mathematics 18 (1995) 223–240MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Reitzinger, S., Schöberl, J.: Algebraic multigrid for edge elements (2000). PreprintGoogle Scholar
  15. 15.
    Weiland, T.: A discretization method for the solution of Maxwell’s equations for six-component fields. Electronics and Communications AEÜ 31 (1977) 116–120Google Scholar
  16. 16.
    Time domain electromagnetic field computation with finite difference methods. Int. J. Num. Mod. 9 (1996) 259–319Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • M. Clemens
    • 1
  • S. Drobny
    • 1
  • M. Wilke
    • 1
  • T. Weiland
    • 1
  1. 1.Darmstadt University of Technology, Fachbereich Elektrotechnik und InformationstechnikFachgebiet Theorie Elektromagnetischer FelderDarmstadtGermany

Personalised recommendations