Comparison of finite element formulations for HTS and ferromagnetic materials

We consider finite element models for high-temperature superconductors and compare two dual formulations, either magnetic-field conforming (H formulation) or magnetic-flux density conforming (A formulation), both with an E(J) power law. The accuracy and efficiency of the formulations are discussed on the basis of the shape of the constitutive law involved in each case. We discuss the performance of each formulation and compare results against benchmarks for superconducting tapes and for bulk trapped-field magnets. We draw general recommendations for the choice of a formulation, an iteration scheme for linearizing the constitutive law, and a time-stepping extrapolation scheme. This approach is extended to soft ferromagnetic materials with a saturation law and we propose a coupled formulation for systems containing both superconductors and ferromagnetic materials. The coupled formulation is shown to be accurate and more efficient than single formulations applied indistinctly to all materials.