A Particle-Particle, Particle-Density (P3D) algorithm for the calculation of electrostatic interactions of particles with slab-like geometry

TL;DR

The paper introduces a fast, accurate P3D algorithm for calculating electrostatic interactions of particles near slab-like surfaces, efficiently handling boundary conditions with a hybrid plane wave and finite element approach.

Contribution

It presents a novel P3D algorithm that combines plane waves and finite elements for efficient electrostatic calculations in slab geometries, improving computational speed and accuracy.

Findings

Computational complexity is O(N_g log N_g) with a small prefactor.

The method accurately models electrostatics with slab boundary conditions.

It effectively separates short and long-range interactions.

Abstract

We present a fast and accurate method to calculate the electrostatic energy and forces of interacting particles with the boundary conditions appropriate to surfaces, i.e periodic in the two directions parallel to the surface and free in the perpendicular direction. In the spirit of the Ewald method the problem is divided into a short range and long range part. The charge density responsible for the long range part is represented by plane waves in the periodic directions and by finite elements in the non-periodic direction. Our method has computational complexity of O(N_g log(N_g)) with a very small prefactor, where N_g is the number of grid points.