P3M algorithm for dipolar interactions
  An extension to the P3M algorithm for electrostatic interactions is presented, that allows to efficiently compute dipolar interactions in periodic boundary conditions. Theoretical estimates for the root-mean square error of the forces, torques and the energy are derived. The applicability of the estimates is tested and confirmed in several numerical examples. A comparison of the computational performance of the new algorithm to state-of-the-art dipolar Ewald summation methods shows a performance crossover from the Ewald method to the dipolar P3M method for as few as 300 dipolar particles. In larger systems, the new algorithm represents a substantial improvement in performance with respect to the dipolar standard Ewald method. 
Juan J. Cerda, V. Ballenegger, O. Lenz and C. Holm