FFT-based Kronecker product approximation to micromagnetic long-range   interactions
  We derive a Kronecker product approximation for the micromagnetic long range interactions in a collocation framework by means of separable sinc quadrature. Evaluation of this operator for structured tensors (Canonical format, Tucker format, Tensor Trains) scales below linear in the volume size. Based on efficient usage of FFT for structured tensors, we are able to accelerate computations to quasi linear complexity in the number of collocation points used in one dimension. Quadratic convergence of the underlying collocation scheme as well as exponential convergence in the separation rank of the approximations is proved. Numerical experiments on accuracy and complexity confirm the theoretical results. 
Lukas Exl, Claas Abert, Norbert J. Mauser, Thomas Schrefl, Hans Peter   Stimming, Dieter Suess
physics.comp-ph math.NA