Journal of Superconductivity and Novel Magnetism

, Volume 28, Issue 8, pp 2345–2354 | Cite as

A Finite Element Simulation Tool for Predicting Hysteresis Losses in Superconductors Using an H-Oriented Formulation with Cohomology Basis Functions

  • Valtteri Lahtinen
  • Antti Stenvall
  • Frédéric Sirois
  • Matti Pellikka
Original Paper


Currently, modelling hysteresis losses in superconductors is most often based on the H-formulation of the eddy current model (ECM) solved using the finite element method (FEM). In the H-formulation, the problem is expressed using the magnetic field intensity H and discretized using edge elements in the whole domain. Even though this approach is well established, it uses unnecessary degrees of freedom (DOFs) and introduces modelling error such as currents flowing in air regions due to finite air resistivity. In this paper, we present a modelling tool utilizing another H-oriented formulation of the ECM, making use of cohomology of the air regions. We constrain the net currents through the conductors by fixing the DOFs related to the so-called cohomology basis functions. As air regions will be truly non-conducting, DOFs and running times of these nonlinear simulations are reduced significantly as compared to the classical H-formulation. This fact is demonstrated through numerical simulations.


Superconductors Hysteresis losses Finite element method Cohomology 



This research was partially supported by The Academy of Finland project #250652. Most of the work leading to this research was conducted during the research exchange period of Valtteri Lahtinen 19.8.2013–15.2.2014 at École Polytechnique de Montréal, Montréal, Canada.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Valtteri Lahtinen
    • 1
    • 2
  • Antti Stenvall
    • 1
  • Frédéric Sirois
    • 2
  • Matti Pellikka
    • 1
    • 3
  1. 1.ElectromagneticsTampere University of TechnologyTampereFinland
  2. 2.Department of Electrical EngineeringÉcole Polytechnique de MontréalMontréalCanada
  3. 3.Microsoft Devices GroupTampereFinland

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