Efficient and accurate three dimensional Poisson solver for surface problems

TL;DR

This paper introduces a highly accurate, efficient three-dimensional Poisson solver optimized for surface problems with mixed boundary conditions, achieving O(N log N) computational complexity suitable for real space electrostatic calculations.

Contribution

The paper presents a novel Poisson solver that combines high accuracy with computational efficiency for surface electrostatics under mixed boundary conditions.

Findings

Achieves O(N log N) computational complexity.

Provides highly accurate electrostatic potentials.

Suitable for real space methods with uniform grids.

Abstract

We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are needed for all kind of surface problems. Our method has an O(N log N) computational cost, where N is the number of grid points, with a very small prefactor. This Poisson solver is primarily intended for real space methods where the charge density and the potential are given on a uniform grid.