Kronecker product approximation of demagnetizing tensors for micromagnetics

A comparison study of the asymptotic behavior between different compression techniques is reported. We show that by applying the Kronecker product approximation, the storage of a three-dimensional demagnetizing tensor with N6N6 entries can be reduced to O(N2)O(N2), showing a superlinear compression behavior. When magnetization and magnetostatic field vectors are stored in compressed forms, a superlinear speedup of a field evaluation is gained.