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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 nonconducting 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 article, we separate the magnetic field into a source and reaction field and use the H-&#x03A6; 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-&#x03A6; formulation is more accurate and efficient than the H-A formulation in 2-D.

ieee transactions on applied superconductivity

Efficient Modeling of High-Temperature Superconductors Surrounded by Magnetic Components Using a Reduced H&#x2013;<inline-formula><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> Formulation

Efficient Modeling of High-Temperature Superconductors Surrounded by Magnetic Components Using a Reduced H–$\phi$ Formulation