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The evaluation of electrostatic energy for a set of point charges in aperiodic lattice is a computationally expensive part of molecular dynamicssimulations (and other applications) because of the long-range nature of theCoulomb interaction. A standard approach is to decompose the Coulomb potentialinto a near part, typically evaluated by direct summation up to a cutoffradius, and a far part, typically evaluated in Fourier space. In practice, alldecomposition approaches involve approximations---such as cutting off thenear-part direct sum---but it may be possible to find new decompositions withimproved tradeoffs between accuracy and performance. Here we present the$\textit{u-series}$, a new decomposition of the Coulomb potential that is moreaccurate than the standard (Ewald) decomposition for a given amount ofcomputational effort, and achieves the same accuracy as the Ewald decompositionwith approximately half the computational effort. These improvements, which wedemonstrate numerically using a lipid membrane system, arise because the$\textit{u}$-series is smooth on the entire real axis and exact up to thecutoff radius. Additional performance improvements over the Ewald decompositionmay be possible in certain situations because the far part of the$\textit{u}$-series is a sum of Gaussians, and can thus be evaluated usingalgorithms that require a separable convolution kernel; we describe one suchalgorithm that reduces communication latency at the expense of communicationbandwidth and computation, a tradeoff that may be advantageous on modernmassively parallel supercomputers.

The $\textit{u}$-series: A separable decomposition for electrostatics computation with improved accuracy