HOW TO MESH UP EWALD SUMS. II. AN ACCURATE ERROR ESTIMATE FOR THE PARTICLE-PARTICLE-PARTICLE-MESH ALGORITHM

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.