A preconditioned Krylov subspace solver for a saddle-point model of a single-phase induction machine

  • H. De Gersem
  • S. Vandewalle
  • K. Hameyer
Conference paper


A time-harmonic model for a single-phase induction machine is constructed consisting of three domains coupled by interface conditions involving Fourier transforms and selection operators. The interface conditions are taken into account by projecting the system onto the space of vectors with matching interface conditions or by a saddle-point formulation with constraint equations.The saddle-point problem is solved by the bi-conjugate gradient stabilised method with a block preconditioner based on a field-circuit coupled algebraic multigrid for the finite element equations and an approximate Schur complement.


Krylov Subspace Eddy Current Effect Finite Element System Magnetic Flux Line Block Preconditioner 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bank, R.E., Welfert, B.D., Yserentant, H. (1990): A class of iterative methods for solving saddle point problems. Numer. Math. 56, 645–666MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Brezzi, E, Fortin, M. (1991): Mixed and hybrid finite element methods. Springer, BerlinMATHCrossRefGoogle Scholar
  3. [3]
    De Gersem, H., Hameyer, K. (2002): Air gap flux splitting for the time-harmonic finite element simulation of single-phase induction machines. IEEE Trans. Magnetics 38, 1221–1224CrossRefGoogle Scholar
  4. [4]
    De Gersem, H., Mertens, R, Pahner, U., Belmans, R, Hameyer, K. (1998): A topological method used for field-circuit coupling. IEEE Trans. Magnetics 34, 3190–3193CrossRefGoogle Scholar
  5. [5]
    Elman, H.C. (1999): Preconditioning for the steady-state Navier-Stokes equations with low viscosity. SIAM J. Sci. Comput. 20, 1299–1316MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Fischer, B., Ramage, A., Silvester, D.J., Wathen, A.J. (1998): Minimum residual methods for augmented systems. BIT 38, 527–543MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Rusten, T., Winther, R. (1992): A preconditioned iterative method for saddlepoint problems. SIAM J. Matrix Anal. Appl. 13, 887–904MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    Stölting, H.-D., Kallenbach, E. (eds.) (2001): Handbuch Elektrische Kleinantriebe. Hanser, MünchenGoogle Scholar
  9. [9]
    Swarztrauber, P.N. (1982): Vectorizing the FFTs. In: Rodrigue, G. (ed.): Parallel computations. Academic Press, Orlando, pp. 51–83Google Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • H. De Gersem
    • 1
  • S. Vandewalle
    • 2
  • K. Hameyer
    • 3
  1. 1.Computational Electromagnetics LaboratoryTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Department of Computer ScienceKatholieke Universiteit LeuvenLeuven-HeverleeBelgium
  3. 3.Division ELEN, Department ESATKatholieke Universiteit LeuvenLeuven-HeverleeBelgium

Personalised recommendations