An O(N) quasi-Ewald splitting method for nanoconfined electrostatics

TL;DR

This paper introduces an efficient O(N) quasi-Ewald splitting method tailored for simulating electrostatics in nanoconfined quasi-2D systems, combining advanced numerical techniques for improved accuracy and computational speed.

Contribution

A novel quasi-Ewald splitting strategy that integrates multiple numerical methods to achieve linear complexity in simulating nanoconfined electrostatics.

Findings

Achieves O(N) computational complexity.

Validates accuracy and efficiency through prototype system simulations.

Highlights phenomena like dielectric boundary effects and anisotropic diffusion.

Abstract

Simulating the dynamics of charged particles in quasi-two-dimensional (quasi-2D) nanoconfined systems presents a significant computational challenge due to the long-range nature of electrostatic interactions and the geometric anisotropy. To address this, we introduce a novel quasi-Ewald splitting strategy tailored for particle-based simulations in such geometry. Our splitting strategy seamlessly integrates a collection of advanced numerical techniques, including optimal quadrature rules [L. N. Trefethen, SIAM Rev. 64(1)(2022), pp.132-150], fast pairwise kernel summation methods [S. Jiang and L. Greengard, Commun. Comput. Phys. 31(1)(2022), pp.1-26], and the random batch method with importance sampling in k-space [S. Jin, L. Li, Z. Xu et al., SIAM J. Sci. Comput. 43(4)(2021), pp.B937-B960]. The resulting algorithm achieves an O(N) overall computational complexity, where N denotes the total number of confined particles. Simulations of several prototype systems validate the accuracy and efficiency of our method. Furthermore, we present numerical observations specifically related to nanoconfined charged many-body systems, highlighting phenomena such as dielectric boundary effects, anisotropic diffusion, and the structure of the electrical double layer (EDL) under conditions of charge asymmetry.