Random Batch Ewald Method for Dielectrically Confined Coulomb Systems

TL;DR

This paper introduces RBE2D, an efficient, scalable method for simulating quasi-2D Coulomb systems with dielectric boundaries, reducing computational cost and handling complex boundary conditions accurately.

Contribution

The paper presents a novel random batch Ewald method for 2D-confined Coulomb systems that is insensitive to aspect ratio and achieves optimal O(N) complexity with reduced polarization costs.

Findings

RBE2D matches PPPM accuracy in simulations.

Significant reduction in computational cost.

Excellent scalability demonstrated in numerical tests.

Abstract

Quasi two-dimensional Coulomb systems have drawn widespread interest. The reduced symmetry of these systems leads to complex collective behaviors, yet simultaneously poses significant challenges for particle-based simulations. In this paper, a novel method is presented for efficiently simulate a collection of charges confined in doubly-periodic slabs, with the extension to scenarios involving dielectric jumps at slab boundaries. Unlike existing methods, the method is insensitive to the aspect ratio of simulation box, and it achieves optimal O(N) complexity and strong scalability, thanks to the random batch Ewald (RBE) approach. Moreover, the additional cost for polarization contributions, represented as image reflection series, is reduced to a negligible cost via combining the RBE with an efficient structure factor coefficient re-calibration technique in k-space. Explicit formulas for optimal parameter choices of the algorithm are provided through error estimates, together with a rigorous proof. Finally, we demonstrate the accuracy, efficiency and scalability of our method, called RBE2D, via numerical tests across a variety of prototype systems. An excellent agreement between the RBE2D and the PPPM method is observed, with a significant reduction in the computational cost and strong scalability, demonstrating that it is a promising method for a broad range of charged systems under quasi-2D confinement.