David J. Hardy, Matthew A. Wolff, Jianlin Xia, Klaus Schulten, and Robert D.
Skeel.
Multilevel summation with B-spline interpolation for pairwise
interactions in molecular dynamics simulations.
Journal of Chemical Physics, 144:114112, 2016.
(16 pages).
(PMC: PMC4808071)
HARD2016
The multilevel summation method
for calculating electrostatic interactions in molecular dynamics simulations
constructs an approximation to a pairwise
interaction kernel and its gradient,
which can be evaluated at a cost
that scales linearly
with the number of
atoms.
The method smoothly splits the kernel into a sum
of partial kernels of increasing range and decreasing variability
with the longer-range parts interpolated from grids of increasing coarseness.
Multilevel summation is especially appropriate
in the context of dynamics and minimization,
because it can produce continuous gradients.
This article explores the use of B-splines to increase the accuracy of the
multilevel summation method
(for nonperiodic boundaries)
without incurring additional computation other than a preprocessing step
(whose cost also scales linearly).
To obtain accurate results efficiently involves technical difficulties,
which are overcome by a novel preprocessing algorithm.
Numerical experiments demonstrate that the resulting method offers
substantial improvements in accuracy
and that its performance is
competitive with
an implementation of the fast multipole method in general
and markedly better for
Hamiltonian formulations of
molecular dynamics.
The improvement is great enough to establish multilevel summation
as a serious contender for calculating pairwise interactions
in molecular dynamics simulations.
In particular, the method
appears to be uniquely capable for molecular dynamics in two situations,
nonperiodic boundary conditions and massively parallel computation,
where the fast Fourier transform employed in the
particle-mesh Ewald method falls short.
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