Assessment of the Computational Performances of the Semi-Analytical Method (SAM) for Computing 2-D Current Distributions in Superconductors

The semi-analytical method (SAM) is a fast integral technique for solving small 2-D, time-transient electromagnetic problems in high temperature superconductors (HTS) with transport current and/or applied field. The method in itself is a generalization of the so-called ldquoBrandt methodrdquo. In order to determine its optimal context of utilization, computation times were compared with those of the finite element method (FEM), for the case of a simple monocore superconducting tape. In order to perform an objective comparison, the same adaptive time step integration algorithm (DASPK) was used in both cases. This algorithm is built-in in the COMSOL Multiphysics package, which served as our benchmark for the FEM, whereas we had to implement it within a compiled version of the SAM based on a C proprietary code. To this end, we used the IDA solver (from the SUNDIALS package), available as a public C code. Comparisons were performed for different ldquonrdquo values for the superconducting material, and for different mesh coarseness. As a result, the SAM proved to be 10 times faster than the FEM for problems involving 300 elements in the mesh (conducting regions only), and showed equal performances with the FEM with 850-900 elements. As the number of element further grows, the SAM looses its advantage over the FEM.