Model files

Alternative to the H-formulation for critical state simulation in HTS materials


This model was shared by Dong Keun Oh, Korea Institute of Fusion Energy.

This model is developed as an attempt of static H-formulation to substitute for the magnetic formulation (A-formulation) of “the self-consistent static critical current model” which has been recognized as an efficient method founded on the idea of domain-wise E-field uniformity in static condition . The idea of static H-formulation is drawn by the “penalized” magnetic vector potential to close the variational from (weak from) of magnetic energy, and the numerical scheme is directly associated with the (divergence-free) vectorial DoFs of magnetic field. Conforming to the weak form in penalization, a well-defined free boundary problem (BEM : Bounday Element Model) is brought together to properly describe the stray field outside of the domain, which is preferable not only to reduce the redundant air mesh around, but also to enable the background field explicitly superposed to the model . The mesh structure of the model (a Roeble cable of 10 HTS strands) is identical to the original model in A-formulation, except for the diameter of air mesh which is reduced significantly; the original model is also included with a minor modification for exact comparison.  All modellings are carried out using FreeFEM++ 4.7-1. Because of the requirement of the BEM plugin, the MPI version of FreeFEM++ has to be applied so that you have to run the model as “ff-mpirun -np 1 file_to_run -wg”. A COMSOL version of the Roebel cable model in H-formulation is also implemented as presented in HTS 2022 Workshop.



  1. Dong Keun Oh, An Alternative in H-Formulation to the Critical Current Model of HTS Conductors, IEEE Transactions on Applied Superconductivity, IEEE Transactions on Applied Superconductivity, volume 32, no. 7, 2022

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