Although the H-formulation has proven to be one of the most versatile formulations used to accurately model superconductors in the finite element method, the use of vector dependent variables in non-conducting regions leads to unnecessarily long computation times. Additionally, in some applications of interest, the combination of multiple magnetic components interacting with superconducting bulks and/or tapes leads to large domains of simulation. In this work, we separate the magnetic field into a source and reaction field and use the H-ϕ formulation to efficiently simulate a superconductor surrounded by magnetic bodies. We model a superconducting cube between a pair of Helmholtz coils and a permanent magnet levitating above a superconducting pellet. In both cases, we find excellent agreement with the H-formulation, while the computation times are reduced by factors of nearly three and four in 2-D and 3-D, respectively. Finally, we show that the H-ϕ formulation is more accurate and efficient than the H-A formulation in 2-D.
@article{arxiv.2104.05582,
title = {Efficient modeling of high temperature superconductors surrounded by magnetic components using a reduced H-$\phi$ formulation},
author = {Alexandre Arsenault and Frédéric Sirois and Francesco Grilli},
journal= {arXiv preprint arXiv:2104.05582},
year = {2021}
}