  Computer simulations of model systems are widely used to explore striking
phenomena in promising applications spanning from physics, chemistry, biology,
to materials science and engineering. The long range electrostatic interactions
between charged particles constitute a prominent factor in determining
structures and states of model systems. How to efficiently calculate
electrostatic interactions in model systems subjected to partial or full
periodic boundary conditions has been a grand challenging task. In the past
decades, a large variety of computational schemes have been proposed, among
which the Ewald summation method is the most reliable route to accurately deal
with electrostatic interactions in model systems. In addition, extensive effort
has been done to improve computational efficiency of the Ewald summation based
methods. Representative examples are approaches based on cutoffs, reaction
fields, multi-poles, multi-grids, and particle-mesh schemes. We sketched an
ENUF method, an abbreviation for the Ewald summation method based on
Non-Uniform fast Fourier transform technique, and have implemented this method
in particle-based simulation packages to calculate electrostatic energies and
forces at micro- and mesoscopic levels. Extensive computational studies of
conformational properties of polyelectrolytes, dendrimer-membrane complexes,
and ionic fluids demonstrated that the ENUF method and its derivatives conserve
both energy and momentum to floating point accuracy, and exhibit a
computational complexity of $\mathcal{O}(N\log N)$ with optimal physical
parameters. These ENUF based methods are attractive alternatives in molecular
simulations where high accuracy and efficiency of simulation methods are needed
to accelerate calculations of electrostatic interactions at extended
spatiotemporal scales.
