P3M algorithm for dipolar interactions.

An extension to the P(3)M 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 a standard dipolar-Ewald summation methods shows a performance crossover from the Ewald method to the dipolar P(3)M 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. Finally, a test comparing point-dipole-based and charged-pair based models shows that point-dipole-based models exhibit a better performance than charged-pair based models.