The three most common methods, Ewald, fast multipole (FMM) and the particle-particle particle-mesh (PPPM), used to compute the interactions in many body Coulombic systems are compared for single and multi-processor machines. The Ewald method is recommended for systems of a few hundred particles per processor or less. For larger systems the PPPM method is suggested. The FMM is slower and more difficult to code efficiently.
@article{arxiv.cond-mat/9511134,
title = {Comments on PPPM, FMM, and the Ewald Method for Large Periodic Coulombic Systems},
author = {E. L. Pollock and Jim Glosli},
journal= {arXiv preprint arXiv:cond-mat/9511134},
year = {2009}
}