How to mesh up Ewald sums (II): An accurate error estimate for the P3M   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. 
Markus Deserno and Christian Holm