David J. Hardy, Zhe Wu, James C. Phillips, John E. Stone, Robert D. Skeel, and
Klaus Schulten.
Multilevel summation method for electrostatic force evaluation.
Journal of Chemical Theory and Computation, 11:766-779, 2015.
(PMC: PMC4325600)
HARD2015
The multilevel summation method (MSM) offers an efficient algorithm
utilizing convolution for evaluating long-range forces arising in molecular
dynamics
simulations.
Shifting the balance of computation and communication, MSM provides
key advantages
over the ubiquitous particle-mesh Ewald (PME) method, offering better
scaling on parallel
computers and permitting more modeling flexibility, with support for
periodic systems like
PME, but also for semi-periodic and non-periodic systems. The version
of MSM available
in the simulation program NAMD is described, and its performance and
accuracy are
compared with the PME method.
The accuracy feasible for MSM in practical applications reproduces PME
results for
water property calculations of density, diffusion constant, dielectric
constant, surface
tension, radial distribution function, and distance-dependent Kirkwood
factor,
even though the numerical accuracy of PME is higher than that of MSM.
Excellent agreement between MSM and PME is found also for interface
potentials of air-
water and membrane-water interfaces, where long-range Coulombic
interactions are
crucial. Applications demonstrate also the suitability of MSM for
systems with semi-
periodic and non-periodic boundaries.
For this purpose, simulations have been performed with periodic
boundaries along
directions parallel to a membrane surface but not along the surface
normal,
yielding membrane pore formation induced by an imbalance of charge
across the
membrane. Using a similar semi-periodic boundary condition, ion
conduction through a
graphene nanopore driven by an ion gradient has been simulated.
Furthermore, proteins
have been simulated inside a single spherical water droplet. Finally,
parallel scalability
results show the ability of MSM to outperform PME when scaling a
system of modest size
(less than 100K atoms) to over a thousand processors, demonstrating
the suitability of
MSM for large-scale parallel simulation.
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