Highly accurate and efficient algorithm for electrostatic interaction of charged particles confined by metallic parallel plates

TL;DR

This paper introduces a highly accurate, efficient algorithm for calculating electrostatic interactions of charged particles confined by metallic parallel plates, suitable for simulations requiring partial periodicity and boundary condition preservation.

Contribution

The authors develop a novel algorithm that maintains boundary conditions without artifacts and achieves quasilinear complexity, improving computational efficiency for electrostatic simulations.

Findings

Accurately computes charge induced on metallic boundaries.

Demonstrates application to sodium chloride ultrathin films.

Achieves $ ext{O}(N ext{log} N)$ complexity in electrostatic calculations.

Abstract

We present an accurate and efficient algorithm to calculate the electrostatic interaction of charged point particles with partially periodic boundary conditions that are confined along the nonperiodic direction by two metallic parallel plates. The method preserves the original boundary conditions and hence, it does not introduce any kind of artifacts. In addition, it enjoys the quasilinear complexity of $\mathcal{O}(N\ln(N))$, where $N$ being the number of particles in the simulation box. In fact, based on the superposition principle in electrostatics, the problem is split into two electrostatic problems where each one can be calculated by the appropriate Poisson solver. In this paper we apply the method to sodium chloride ultrathin films and investigate its dielectric response with respect to external bias voltage. We show how accurately in this method one can obtain the total charge induced on metallic boundaries to an arbitrary precision.