Numerical simulation of the magnetization of high-temperature superconductors: a 3D finite element method using a single time-step iteration
In this paper, we report progress towards a 3D finite element model for the magnetization of a high-temperature superconductor (HTS): we suggest a method that takes into account a power law conductivity and demagnetization effects, while neglecting the effects associated with currents that are not perpendicular to the local magnetic induction. We consider samples that are subjected to a uniform magnetic field varying linearly with time. Their magnetization is calculated by means of a weak formulation in the magnetostatic approximation of the Maxwell equations (A– formulation). An implicit method is used for the temporal resolution (backward Euler scheme) and is solved with the open source solver GetDP. Fixed point iterations are used to deal with the power law conductivity of HTS. The finite element formulation is validated for an HTS tube with large n value by comparing with results obtained with other well-established methods. We show that carrying out the calculations with a single time-step (as opposed to many small time-steps) produces results with excellent accuracy in a drastically reduced simulation time. The numerical method is extended to the study of the trapped magnetization of cylinders that are drilled with different arrays of columnar holes arranged parallel to the cylinder axis.