Large-scale electromagnetic field analyses of coils wound with coated conductors using a current-vector-potential formulation with a thin-strip approximation

We developed a novel software for large-scale electromagnetic field analyses of coils wound with coated conductors based on current-vector-potential formulation with thin-strip approximation. Although this formulation was effective for obtaining the precise solutions of the electromagnetic field, the strong nonlinear property of superconducting materials frequently led to highly ill-conditioned linear systems of equations, which were difficult to solve efficiently. Moreover, the memory consumption and computation time required for the analyses rapidly increased with the size of the analysis due to dense matrix operations. In our software, the first difficulty was addressed by a novel preconditioning technique based on the algebraic multigrid method. Algebraic multigrid preconditioning enabled us to efficiently and stably solve the ill-conditioned linear systems of equations encountered in our analyses. It also improved the robustness of the analyses containing multifilament-coated conductors. As regards the second difficulty, the hierarchical matrices representation drastically reduced the memory consumption related to the dense matrices, as well as computation time. Meanwhile, our implementation of the hierarchical matrices representation was quite compatible with parallel computations on distributed memory computers. Finally, we presented some practical examples of large-scale analyses, which became possible by using the new software. For instance, the analysis of a cosine-theta dipole magnet whose number of degrees of freedom was more than 1.5 million was successfully completed in 78 h by 56 parallel processes and with a total memory consumption of 177 GB.