An \({{\mathcal{O}}(N)}\) Quasi-Ewald Splitting Method for Nanoconfined Electrostatics

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 this geometry. Our splitting strategy seamlessly integrates a collection of advanced numerical techniques, including optimal quadrature rules [L. N. Trefethen, SIAM Rev., 64 (2022), pp. 132–150], fast pairwise kernel summation methods [S. Jiang and L. Greengard, Commun. Comput. Phys., 31 (2022), pp. 1–26], and the random batch method with importance sampling in [Formula: see text]-space [S. Jin et al., SIAM J. Sci. Comput., 43 (2021), pp. B937–B960]. The resulting algorithm achieves an [Formula: see text] overall computational complexity, where [Formula: see text] 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.