A survey of the parallel performance and the accuracy of Poisson solvers for electronic structure calculations

TL;DR

This paper surveys various Poisson solvers used in electronic structure calculations, analyzing their parallel performance and accuracy to guide large-scale computational applications.

Contribution

It provides a comprehensive comparison of Poisson solvers' performance and accuracy, including implementation details in the Octopus code for large system simulations.

Findings

Highly parallelizable routines enable large system calculations

Performance varies significantly among different Poisson solvers

The analysis guides the selection of suitable solvers for electronic structure computations

Abstract

We present an analysis of different methods to calculate the classical electrostatic Hartree potential created by charge distributions. Our goal is to provide the reader with an estimation on the performance ---in terms of both numerical complexity and accuracy--- of popular Poisson solvers, and to give an intuitive idea on the way these solvers operate. Highly parallelisable routines have been implemented in the first-principle simulation code Octopus to be used in our tests, so that reliable conclusions about the capability of methods to tackle large systems in cluster computing can be obtained from our work.