Comments on PPPM, FMM, and the Ewald Method for Large Periodic Coulombic Systems

TL;DR

This paper compares Ewald, FMM, and PPPM methods for Coulombic systems, recommending Ewald for small systems, PPPM for larger ones, and noting FMM's slower performance and coding complexity.

Contribution

It provides a comparative analysis of three popular Coulomb interaction computation methods for different system sizes and computing architectures.

Findings

Ewald is best for systems with fewer than a few hundred particles per processor.

PPPM is recommended for larger systems.

FMM is slower and more complex to implement.

Abstract

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.