Accelerating Molecular Dynamics Simulations using Fast Ewald Summation with Prolates

TL;DR

The paper introduces ESP, a novel Ewald summation method using prolate spheroidal wave functions, which significantly accelerates long-range electrostatic calculations in molecular dynamics simulations with minimal accuracy loss.

Contribution

ESP provides a more efficient Fourier representation for Ewald summation, reducing computational costs and improving scalability in MD simulations, and is integrated into popular MD packages.

Findings

ESP achieves roughly 3-fold acceleration over PME/PPPM at moderate accuracy.

At high accuracy, ESP offers up to 10-fold speed-up in electrostatics calculations.

ESP improves strong scaling and is validated in realistic biological and material simulations.

Abstract

The evaluation of long-range Coulomb interactions is a significant cost in molecular dynamics (MD), even when using Particle Mesh Ewald (PME) or Particle-Particle-Particle-Mesh (PPPM) methods, which rely on Ewald splitting and the fast Fourier transform to achieve near-linear scaling. We introduce ESP -- Ewald summation with prolate spheroidal wave functions (PSWFs) -- which leads to a more efficient Fourier representation and a reduction in the required grid size, global communication, and particle-grid operations, without loss of accuracy. We have integrated the ESP method into two widely-used open-source MD packages, LAMMPS and GROMACS, enabling rapid comparison and adoption. Relative to PME/PPPM baselines at error tolerances $10^{-3}$ to $10^{-4}$, ESP gives roughly a $3$-fold acceleration of electrostatic interactions, and a $2.5$-fold speed-up in the MD simulation when using about $10^3$ compute cores. At high accuracy ($10^{-5}$), these increase to $10$-fold for the far-field electrostatics and $5$-fold for MD simulation. Furthermore, we show that the accelerated codes have improved strong scaling with core count, and validate them in realistic long-time biological and material simulations. ESP thus offers a practical, drop-in path to reduce the time-to-solution and energy footprint of MD workflows.