P3M algorithm for dipolar interactions

TL;DR

This paper introduces an extended P3M algorithm tailored for efficient computation of dipolar interactions under periodic boundary conditions, with theoretical error estimates and demonstrated performance advantages over traditional Ewald methods.

Contribution

The paper develops a novel P3M algorithm specifically for dipolar interactions, including error analysis and performance comparison with existing methods.

Findings

The new algorithm accurately estimates force, torque, and energy errors.

Performance crossover occurs at around 300 particles.

Significant efficiency improvements in large systems.

Abstract

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.