What Formulation Should One Choose for Modeling a 3-D 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 3-D 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 (DOFs), 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.