Implementation of the H-φ Formulation in COMSOL Multiphysics for Simulating the Magnetization of Bulk Superconductors and Comparison With the H-Formulation

The H-formulation, used abundantly for the simulation of high-temperature superconductors, has shown to be a very versatile and easily implementable way of modeling electromagnetic phenomena involving superconducting materials. However, the simulation of a full vector field in current-free domains unnecessarily adds degrees of freedom to the model, thereby increasing computation times. In this contribution, we implement the well-known H-phi formulation in COMSOL multiphysics in order to compare the numerical performance of the H and H-phi formulations in the context of computing the magnetization of bulk superconductors. We showthat the H-phi formulation can reduce the number of degrees of freedom and computation times by nearly a factor of two for a given relative error. The accuracy of the magnetic fields obtained with both formulations are demonstrated to be similar. The computational benefits of the H-phi formulation are shown to far outweigh the added complexity of its implementation, especially in 3-D. Finally, we identify the ideal element orders for both H and H-f formulations to be quartic in 2-D and cubic in 3-D, corresponding to the highest element orders implementable in COMSOL.

Automated summary

The H-phi formulation is an effective method for modeling electromagnetic phenomena involving superconducting materials, showing better performance in computation compared to the H formulation by significantly reducing degrees of freedom and computation times. The accuracy of magnetic fields obtained with both formulations are similar, but the computational benefits of the H-phi formulation outweigh its complexity.