A Fast Integral Equation $J-\varphi$ Formulation for Superconducting Structures

This article presents an integral equation method based on the current–potential (
$\mathbf {J}-\varphi _{e}$
) formulation, for the solution of the eddy currents problem in superconducting structures. Two efficient methods for storing and manipulating the fully populated matrices resulting from the discretization of the integral equation are proposed in this work. These approaches leverage hierarchical (
$\mathcal {H}$
) matrices and the fast Fourier transform technique, tailored for voxelized structures. These techniques drastically reduce the computational cost of the numerical simulations. The proposed approach is compared to existing methods, as the
$\mathbf {H}-\varphi _{m}$
formulation, and is efficiently applied to calculate the power losses for a realistic high-temperature superconductor coil.