HOW TO MESH UP EWALD SUMS - I - A THEORETICAL AND NUMERICAL COMPARISON OF VARIOUS PARTICLE MESH ROUTINES

Standard Ewald sums, which calculate, e.g., the electrostatic energy o r the force in periodically closed systems of charged particles, can b e efficiently speeded up by the use of the fast Fourier transformation (FFT). In this article we investigate three algorithms for the FFT-ac celerated Ewald sum, which have attracted widespread attention, namely , the so-called particle-particle -particle mesh ((PM)-M-3), particle mesh Ewald (PME), and smooth PME method. We present a unified view of the underlying techniques and the various ingredients which comprise t hose routines. Additionally, we offer detailed accuracy measurements, which shed some light on the influence of several tuning parameters an d also show that the existing methods - although similar in spirit - e xhibit remarkable differences in accuracy. We propose a set of combina tions of the individual components, mostly relying on the (PM)-M-3 app roach, that we regard to be the most flexible. The issue of estimating the errors connected with particle mesh routines is reserved to paper II. (C) 1998 American Institute of Physics.