Hybrid Formulations and Discretisations for Magnetoquasistatic Models

  • Herbert De Gersem
  • Stephan Koch
  • Thomas Weiland
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)


This paper aims at increasing the modelling flexibility for magnetoquasistatic finite element simulations by allowing different formulations and different discretisation techniques in distinct model regions. Special care is necessary when conceiving algebraic solution techniques for the coupled systems of equations.


Conjugate Gradient Collocation Point Hybrid Formulation Magnetic Vector Potential Beam Tube 
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.


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  1. 1.
    Brenner, S., Scott, L.: The Mathematical Theory of Finite Element Methods. Springer, New York (1996)Google Scholar
  2. 2.
    De Gersem, H., Koch, S., Weiland, T.: Accounting for end effects when calculating eddy currents in thin conductive beam tubes. IEEE Trans. Magn. 45(3), 1040–1043 (2009)Google Scholar
  3. 3.
    Elman, H., Silvester, D., Wathen, A.: Iterative methods for problems in computational fluid dynamics. Tech. Rep. NA-96/19, Oxford University Computing Laboratory (1996)Google Scholar
  4. 4.
    Fischer, B., Ramage, A., Silvester, D., Wathen, A.: Minimum residual methods for augmented systems. BIT 38(3), 527–543 (1998)Google Scholar
  5. 5.
    Fornberg, B.: A Practical Guide to Pseudospectral Methods. Cambridge University Press, Cambridge (1996)Google Scholar
  6. 6.
    Freund, R., Nachtigal, N.: A new Krylov-subspace method for symmetric indefinite linear systems. In: Ames, W. (ed.) Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, pp. 1253–1256 (1994)Google Scholar
  7. 7.
    Koch, S., Trommler, J., De Gersem, H., Weiland, T.: Modeling thin conductive sheets using shell elements in magnetoquasistatic field simulations. IEEE Trans. Magn. 45(3), 1292–1295 (2009)Google Scholar
  8. 8.
    Kovalenko, A., Kalimov, A., Khodzhibagiyan, H., Moritz, G., Mühle, C.: Optimization of a superferric nuclotron type dipole for the GSI fast pulsed synchrotron. IEEE Trans. Appl. Superconduct. 12(1), 161–165 (2002)Google Scholar
  9. 9.
    Krähenbühl, L., Muller, D.: Thin layers in electrical engineering. Example of shell models in analyzing eddy-currents by boundary and finite element methods. IEEE Trans. Magn. 29(5), 1450–1455 (1993)Google Scholar
  10. 10.
    Kurz, S., Russenschuck, S., Siegel, N.: Accurate calculation of fringe fields in the LHC main dipoles. IEEE Trans. Appl. Superconduct. 10(1), 85–88 (2000)Google Scholar
  11. 11.
    Nakata, T., Takahashi, N., Fujiwara, K., Shiraki, Y.: 3-D magnetic field analysis using special elements. IEEE Trans. Magn. 26(5), 2379–2381 (1990)Google Scholar
  12. 12.
    Paige, C., Saunders, M.: Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12(4), 617–629 (1975)Google Scholar
  13. 13.
    Reitzinger, S., Schöberl, J.: An algebraic multigrid method for finite element discretizations with edge elements. Numer. Math. 9(3), 223–238 (2002)Google Scholar
  14. 14.
    Ren, Z.: T-ω formulation for eddy-current problems in multiply connected regions. IEEE Trans. Magn. 38(2), 557–560 (2002)Google Scholar
  15. 15.
    Silvester, P., Ferrari, R.: Finite Elements for Electrical Engineers, 2nd edn. Cambridge University Press, Cambridge (1996)Google Scholar
  16. 16.
    Smith, B., Bjørstad, P., Gropp, W.: Domain Decomposition: Parallel multilevel methods for elliptic partial differential equations. Cambridge University Press, Cambridge (1996)Google Scholar
  17. 17.
    Trefethen, L.: Spectral Methods in Matlab. SIAM, Philadelphia (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Herbert De Gersem
    • 1
  • Stephan Koch
    • 2
  • Thomas Weiland
    • 2
  1. 1.Wave Propagation and Signal Processing Research GroupKatholieke Universiteit LeuvenKortrijkBelgium
  2. 2.Institut für Theorie Elektromagnetischer FelderTechnische Universität DarmstadtDarmstadtGermany

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