COMSOL implementation of the H-$\phi$-formulation with thin cuts for modeling superconductors with transport currents

TL;DR

This paper introduces a COMSOL implementation of the H-$$-formulation with thin cuts, enabling faster and accurate modeling of superconductors with transport currents by simplifying non-conducting domains.

Contribution

It presents a novel method using thin cuts to implement the H-$$-formulation in COMSOL, improving computational efficiency for superconductor simulations.

Findings

H-$$-formulation can be up to seven times faster than H-formulation.

Results show very good agreement with existing formulations.

Method is easily implementable in COMSOL for 2D and 3D models.

Abstract

Despite the acclaimed success of the magnetic field (H) formulation for modeling the electromagnetic behavior of superconductors with the finite element method, the use of vector-dependent variables in non-conducting domains leads to unnecessarily long computation times. In order to solve this issue, we have recently shown how to use a magnetic scalar potential together with the H-formulation in the COMSOL Multiphysics environment to efficiently and accurately solve for the magnetic field surrounding superconducting domains. However, from the definition of the magnetic scalar potential, the non-conducting domains must be made simply connected in order to obey Ampere's law. In this work, we use thin cuts to apply a discontinuity in $\phi$ and make the non-conducting domains simply connected. This approach is shown to be easily implementable in the COMSOL Multiphysics finite element program, already widely used by the applied superconductivity community. We simulate three different models in 2-D and 3-D using superconducting filaments and tapes, and show that the results are in very good agreement with the H-A and H-formulations. Finally, we compare the computation times between the formulations, showing that the H-$\phi$-formulation can be up to seven times faster than the standard H-formulation in certain applications of interest.