Efficient Modeling of High-Temperature Superconductors Surrounded by Magnetic Components Using a Reduced H-φ Formulation

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-phi 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-phi formulation is more accurate and efficient than the H-A formulation in 2-D.

Automated summary

This article presents a method to efficiently simulate superconductors surrounded by magnetic bodies using the H-phi formulation, which significantly reduces computation times compared to the H-formulation, with nearly three times and four times reduction in 2-D and 3-D, respectively. The H-phi formulation is shown to be more accurate and efficient in 2-D compared to the H-A formulation.