A random batch Ewald method for charged particles in the isothermal-isobaric ensemble

TL;DR

The paper introduces a scalable random batch Ewald method for simulating charged particles in the NPT ensemble, significantly reducing computational costs while maintaining accuracy, and demonstrates its effectiveness in molecular dynamics simulations.

Contribution

A novel random batch Ewald method integrated into LAMMPS that reduces computational complexity from quadratic to linear for charged particle simulations in the NPT ensemble.

Findings

Achieves accurate results for water and membrane systems.

Reduces computational cost from O(N^2) to O(N).

Demonstrates high CPU efficiency on supercomputers.

Abstract

We develop an accurate, highly efficient and scalable random batch Ewald (RBE) method to conduct simulations in the isothermal-isobaric ensemble (the NPT ensemble) for charged particles in a periodic box. After discretizing the Langevin equations of motion derived using suitable Lagrangians, the RBE method builds the mini-batch strategy into the Fourier space in the Ewald summation for the pressure and forces so the computational cost is reduced from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ per time step. We implement the method in the LAMMPS package and report accurate simulation results for both dynamical quantities and statistics for equilibrium for typical systems including all-atom bulk water and a semi-isotropic membrane system. Numerical simulations on massive supercomputing cluster are also performed to show promising CPU efficiency of RBE.