Coupled Heat-Electromagnetic Simulation of Inductive Charging Stations for Electric Vehicles

  • Christof KaufmannEmail author
  • Michael Günther
  • Daniel Klagges
  • Matthias Richwin
  • Sebastian Schöps
  • E. Jan W. ter Maten
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 19)


Coupled electromagnetic-heat problems have been studied for induction or inductive heating, for dielectric heating, for testing of corrosion, for detection of cracks, for hardening of steel, and more recently for inductive charging of electric vehicles. In nearly all cases a simple co-simulation is made where the electromagnetics problem is solved in the frequency domain (and which thus is assumed to be linear) and the heat equation in the time domain. One exchanges data after each time step (or after some change in the heat profile). However, the coupled problem is non-linear in the heat variable. In this paper we propose to split the time domain in windows in which we solve the electromagnetics problem in frequency domain. We strengthen the coupling by iterations, for which we prove convergence. By this we obtain a higher accuracy, which will allow for larger time steps and also for higher order time integration. This fully exploits the multirate behavior of the coupled system. An industrial example illustrates the analysis.


Heat Equation Electric Vehicle Eddy Current Loss Source Current Density Magnetic Vector Potential 
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This work is supported by the German BMBF in the context of the SOFA project (grant number 03MS648E). The fifth author is supported by the Excellence Initiative of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universität Darmstadt.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Christof Kaufmann
    • 1
    Email author
  • Michael Günther
    • 2
  • Daniel Klagges
    • 3
  • Matthias Richwin
    • 3
  • Sebastian Schöps
    • 4
  • E. Jan W. ter Maten
    • 2
    • 5
  1. 1.Hochschule Bochum, Fachbereich Elektrotechnik und InformatikBochumGermany
  2. 2.Fachbereich C, Lehrstuhl für Angewandte Mathematik/Numerische AnalysisBergische Universität WuppertalWuppertalGermany
  3. 3.Leopold Kostal GmbH & Co. KGLüdenscheidGermany
  4. 4.Graduate School of Computational EngineeringTechnische Universität DarmstadtDarmstadtGermany
  5. 5.Department of Mathematics & Computer ScienceTU Eindhoven, CASAEindhovenThe Netherlands

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