What Formulation Should One Choose for Modeling a 3D HTS Motor Pole with Ferromagnetic Materials?

We discuss the relevance of several finite-element formulations for nonlinear
systems containing high-temperature superconductors (HTS) and ferromagnetic
materials (FM), in the context of a 3D motor pole model. The formulations are
evaluated in terms of their numerical robustness and efficiency. We propose a
coupled h-phi-a-formulation as an optimal choice, modeling the problem with an
a-formulation in the FM and an h-phi-formulation in the remaining domains.
While maintaining a low number of degrees of freedom, the h-phi-a-formulation
guarantees a robust resolution and strongly reduces the number of iterations
required for handling the nonlinearities of HTS and FM compared to standard
formulations.