TCB Publications - Abstract

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.

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