Abstract
Standard Ewald sums, which calculate e.g. the electrostatic energy
or the force in periodically closed systems of charged particles,
can be efficiently speeded up by the use of the Fast Fourier Transformation
(FFT). In this article we investigate three algorithms for the FFT-accelerated
Ewald sum, which attracted a widespread attention, namely, the so-called
particle-particle--particle-mesh (P$^3$M), particle mesh Ewald
(PME) and smooth PME method. We present a unified view of the underlying
techniques and the various ingredients which comprise those routines.
Additionally, we offer detailed accuracy measurements, which shed
some light on the influence of several tuning parameters and also
show that the existing methods -- although similar in spirit -- exhibit
remarkable differences in accuracy. We propose combinations of the
individual components, mostly relying on the P$^3$M approach, which
we regard as most flexible. The issue of estimating the errors connected
with particle mesh routines is reserved to part II of this series.
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