DAE-Index and Convergence Analysis of Lumped Electric Circuits Refined by 3-D Magnetoquasistatic Conductor Models

  • Sebastian SchöpsEmail author
  • Andreas Bartel
  • Herbert De Gersem
  • Michael Günther
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 14)


In this paper the field/circuit coupling is reconsidered for (non-linear) lumped electric circuits refined by 3-D magnetoquasistatic conductor models, where the circuit is described by modified nodal analysis and the field is discretized in terms of the finite integration technique. This leads to the coupling of systems of differential-algebraic equations, for which two numerical approaches are proposed, the weak coupling (co-simulation) and strong coupling (monolithic). The DAE-index of the subproblems and of the full problem are analyzed, then convergence properties of the co-simulation are studied. Finally computational results of a simple half rectifier circuit are exemplarily given to prove the applicability of the concepts.


Electric Circuit Conductor Model Conductivity Matrix Magnetic Vector Potential Node Potential 
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.
    Benderskaya, G. et al.: Transient Field-Circuit Coupled Formulation Based on the FIT and a Mixed Circuit Formulation. COMPEL 23(4), 968 – 976 (2004)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Dreher, T., Meunier, G.: 3D Line Current Model of Coils and External Circuits. IEEE Trans. Mag. 31(3), 1853 – 1856 (1995)CrossRefGoogle Scholar
  3. 3.
    Bedrosian, G.: A New Method for Coupling Finite Element Field Solutions with External Circuits and Kinematics. IEEE Trans. Mag. 29(2), 1664 – 1668 (1993)CrossRefGoogle Scholar
  4. 4.
    Günther, M., Rentrop, P.: Numerical Simulation of Elec. Circuits. GAMM 1/2, 51 – 77 (2000)Google Scholar
  5. 5.
    Hairer, E., Wanner, G.: Solving ODEs II. Springer, Berlin, 1991Google Scholar
  6. 6.
    Estévez Schwarz, D., Tischendorf, C.: Structural Analysis of Electric Circuits and Consequences for MNA. Int. J. Circ. Theor. Appl. 28(2), 131 – 162 (2000)zbMATHCrossRefGoogle Scholar
  7. 7.
    Bossavit, A.: Computational Electromagnetism. Academic Press, San Diego (1998)zbMATHGoogle Scholar
  8. 8.
    Clemens, M.: Large Systems of Equations in a Discrete Electromagnetism: Formulations and Numerical Algorithms. IEE Proc Sci Meas Tech 152(2), 50 – 72 (2005)CrossRefGoogle Scholar
  9. 9.
    De Gersem, H. et al.: Field-circuit Coupled Models in Electromagnetic Simulation. JCAM 168(1-2), 125 – 133 (2004)zbMATHGoogle Scholar
  10. 10.
    Kettunen, L. et al.: Gauging in Whitney Spaces. IEEE Trans. Mag. 35(3), 1466 – 1469 (1999)CrossRefGoogle Scholar
  11. 11.
    Brenan, K.E. et al.: Numerical Solution of IVPs in DAEs. SIAM, Philadelphia, 1996Google Scholar
  12. 12.
    Arnold, M. et al.: Errors in the Numerical Solution of Nonlinear Differential-Algebraic Systems of Index 2. Martin-Luther-University Halle (1995)Google Scholar
  13. 13.
    Arnold, M., Günther, M.: Preconditioned Dynamic Iteration for Coupled Differential-Algebraic Systems. BIT 41(1), 1 – 25 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Bartel, A.: Partial Differential-Algebraic Models in Chip Design - Thermal and Semiconductor Problems. Ph.D. thesis, TU Karlsruhe, VDI Verlag (2004)Google Scholar
  15. 15.
    Lange, E. et al.: A Circuit Coupling Method Based on a Temporary Linearization of the Energy Balance of the Finite Element Model. IEEE Trans. Mag. 44(6), 838 – 841 (2008)CrossRefGoogle Scholar
  16. 16.
    Zhou, P. et al.: A General Co-Simulation Approach for Coupled Field-Circuit Problems. IEEE Trans. Mag. 42(4), 1051 – 1054 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sebastian Schöps
    • 1
    Email author
  • Andreas Bartel
    • 1
  • Herbert De Gersem
    • 2
  • Michael Günther
    • 1
  1. 1.BU WuppertalWuppertalGermany
  2. 2.KU LeuvenLeuvenBelgium

Personalised recommendations