2,421 research outputs found
Multiple Staggered Mesh Ewald: Boosting the Accuracy of the Smooth Particle Mesh Ewald Method
The smooth particle mesh Ewald (SPME) method is the standard method for
computing the electrostatic interactions in the molecular simulations. In this
work, the multiple staggered mesh Ewald (MSME) method is proposed to boost the
accuracy of the SPME method. Unlike the SPME that achieves higher accuracy by
refining the mesh, the MSME improves the accuracy by averaging the standard
SPME forces computed on, e.g. , staggered meshes. We prove, from theoretical
perspective, that the MSME is as accurate as the SPME, but uses times
less mesh points in a certain parameter range. In the complementary parameter
range, the MSME is as accurate as the SPME with twice of the interpolation
order. The theoretical conclusions are numerically validated both by a uniform
and uncorrelated charge system, and by a three-point-charge water system that
is widely used as solvent for the bio-macromolecules
Development and application of a particle-particle particle-mesh Ewald method for dispersion interactions
For inhomogeneous systems with interfaces, the inclusion of long-range
dispersion interactions is necessary to achieve consistency between molecular
simulation calculations and experimental results. For accurate and efficient
incorporation of these contributions, we have implemented a particle-particle
particle-mesh (PPPM) Ewald solver for dispersion () interactions into
the LAMMPS molecular dynamics package. We demonstrate that the solver's
scaling behavior allows its application to large-scale
simulations. We carefully determine a set of parameters for the solver that
provides accurate results and efficient computation. We perform a series of
simulations with Lennard-Jones particles, SPC/E water, and hexane to show that
with our choice of parameters the dependence of physical results on the chosen
cutoff radius is removed. Physical results and computation time of these
simulations are compared to results obtained using either a plain cutoff or a
traditional Ewald sum for dispersion.Comment: 31 pages, 9 figure
Fast and spectrally accurate summation of 2-periodic Stokes potentials
We derive a Ewald decomposition for the Stokeslet in planar periodicity and a
novel PME-type O(N log N) method for the fast evaluation of the resulting sums.
The decomposition is the natural 2P counterpart to the classical 3P
decomposition by Hasimoto, and is given in an explicit form not found in the
literature. Truncation error estimates are provided to aid in selecting
parameters. The fast, PME-type, method appears to be the first fast method for
computing Stokeslet Ewald sums in planar periodicity, and has three attractive
properties: it is spectrally accurate; it uses the minimal amount of memory
that a gridded Ewald method can use; and provides clarity regarding numerical
errors and how to choose parameters. Analytical and numerical results are give
to support this. We explore the practicalities of the proposed method, and
survey the computational issues involved in applying it to 2-periodic boundary
integral Stokes problems
Accelerating scientific codes by performance and accuracy modeling
Scientific software is often driven by multiple parameters that affect both
accuracy and performance. Since finding the optimal configuration of these
parameters is a highly complex task, it extremely common that the software is
used suboptimally. In a typical scenario, accuracy requirements are imposed,
and attained through suboptimal performance. In this paper, we present a
methodology for the automatic selection of parameters for simulation codes, and
a corresponding prototype tool. To be amenable to our methodology, the target
code must expose the parameters affecting accuracy and performance, and there
must be formulas available for error bounds and computational complexity of the
underlying methods. As a case study, we consider the particle-particle
particle-mesh method (PPPM) from the LAMMPS suite for molecular dynamics, and
use our tool to identify configurations of the input parameters that achieve a
given accuracy in the shortest execution time. When compared with the
configurations suggested by expert users, the parameters selected by our tool
yield reductions in the time-to-solution ranging between 10% and 60%. In other
words, for the typical scenario where a fixed number of core-hours are granted
and simulations of a fixed number of timesteps are to be run, usage of our tool
may allow up to twice as many simulations. While we develop our ideas using
LAMMPS as computational framework and use the PPPM method for dispersion as
case study, the methodology is general and valid for a range of software tools
and methods
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