Hüseyin Kaya, David J. Hardy, and Robert D. Skeel.
Multilevel summation for periodic electrostatics using B-splines.
Journal of Chemical Physics, 154:144105, 2021.
(PMC: PMC8036131)
KAYA2021-DH
Fast methods for calculating 2-body interactions have many
applications, and, for molecular science and cosmology, it is common
to
employ periodic boundary conditions. However, for the 1/r potential,
the energy and forces are ill defined. Adopted here is the model given
by classic Ewald sum. For the fast calculation of 2-body forces, the
most celebrated method is the fast multipole method and its tree-code
predecessor. However, molecular simulations typically employ mesh-
based
approximations and the fast Fourier transform. Both types of methods
have significant drawbacks, which, in most respects, are overcome by
the less well known multilevel summation method (MSM). Presented here
is a realization of the MSM, which can be regarded as a multilevel
extension of the (smoothed) particle–mesh Ewald (PME) method, but with
the Ewald softening replaced by one having a finite range. The 2-level
(single-grid) version of MSM requires fewer tuning parameters than PME
and is marginally faster. Additionally, higher-level versions of MSM
scale well to large numbers of processors, whereas PME and other 2-
level methods do not. Although higher-level versions of MSM are less
efficient on a single processor than the 2-level version, evidence
suggests that they are more efficient than other methods that scale
well, such as the fast multipole method and tree codes.
