How to mesh up Ewald sums (II): An accurate error estimate for the P3M algorithm

TL;DR

This paper develops an accurate error estimate for the P3M algorithm's force calculations, enabling optimal parameter selection and improved simulation accuracy in particle systems.

Contribution

It extends existing error measures to provide a precise, analytic approximation for the P3M algorithm's force error, facilitating better parameter tuning.

Findings

The error estimate closely matches actual force errors in tests.

The analytic approximation simplifies optimal parameter determination.

The method improves force accuracy prediction in particle simulations.

Abstract

We construct an accurate estimate for the root mean square force error of the particle-particle-particle-mesh (P3M) algorithm by extending a single particle pair error measure which has been given by Hockney and Eastwood. We also derive an easy-to-use analytic approximation to the error formula. This allows a straightforward and precise determination of the optimal splitting parameter (as a function of system specifications and P3M parameters) and hence knowledge of the force accuracy prior to the actual simulation. The high quality of the estimate is demonstrated in several examples.