Fast and scalable evaluation of pairwise potentials

Abstract

Pair potentials or kernels, ψ(|r|), play a critical role in a number of areas; these include biophysics, electrical engineering, fluid dynamics, diffusion physics, solid state physics, and many more. The need to evaluate these potentials rapidly for N particles gives rise to the classical N-body problem. In this paper, we present scalable parallel algorithms for evaluation of these potentials for highly non-uniform distributions. The underlying methodology for evaluating these potentials relies on the accelerated Cartesian expansion (ACE) framework that is quasi-kernel-independent with the requirement that the kernel be differentiable with known derivatives. The results presented demonstrate the accuracy control, low cost, and parallel scalability offered by this method for several example kernels and distributions of up to 5 billion particles on 16384 CPU cores. Potential applications of the algorithm include various disciplines of computational physics, engineering, machine learning, among others.