Efficient and accurate solver of the three-dimensional screened and unscreened Poisson's equation with generic boundary conditions

TL;DR

This paper introduces a versatile, accurate, and efficient 3D Poisson solver that handles various boundary conditions and screening lengths, with linear scaling and no adjustable parameters, suitable for advanced materials simulations.

Contribution

The paper presents a novel explicit solver combining plane-wave and interpolating scaling functions, capable of handling diverse boundary conditions and screening lengths with simple grid refinement.

Findings

Achieves O(N log N) computational scaling.

Validated on model systems for accuracy.

Handles arbitrary boundary conditions and screening lengths.

Abstract

We present an explicit solver of the three-dimensional screened and unscreened Poisson's equation which combines accuracy, computational efficiency and versatility. The solver, based on a mixed plane-wave / interpolating scaling function representation, can deal with any kind of periodicity (along one, two, or three spatial axes) as well as with fully isolated boundary conditions. It can seamlessly accommodate a finite screening length, non-orthorhombic lattices and charged systems. This approach is particularly advantageous because convergence is attained by simply refining the real space grid, namely without any adjustable parameter. At the same time, the numerical method features O(N log N) scaling of the computational cost (N being the number of grid points) very much like plane-wave methods. The methodology, validated on model systems, is tailored for leading-edge computer simulations of materials (including ab initio electronic structure computations), but it might as well be beneficial for other research domains.