Highly Parallel Demagnetization Field Calculation Using the Fast   Multipole Method on Tetrahedral Meshes with Continuous Sources
  The long-range magnetic field is the most time-consuming part in micromagnetic simulations. Improvements both on a numerical and computational basis can relief problems related to this bottleneck. This work presents an efficient implementation of the Fast Multipole Method [FMM] for the magnetic scalar potential as used in micromagnetics. We assume linearly magnetized tetrahedral sources, treat the near field directly and use analytical integration on the multipole expansion in the far field. This approach tackles important issues like the vectorial and continuous nature of the magnetic field. By using FMM the calculations scale linearly in time and memory. 
Pietro Palmesi, Lukas Exl, Florian Bruckner, Claas Abert, Dieter Suess
physics.comp-ph