Three real-space discretization techniques in electronic structure calculations

TL;DR

This paper compares three real-space discretization techniques—finite-difference, finite-elements, and wavelets—for electronic structure calculations, highlighting their principles, applications, and differences.

Contribution

It provides a comprehensive review and comparison of three major discretization methods used in electronic structure calculations, based on multiple code development projects.

Findings

Finite-difference, finite-elements, and wavelets each have unique advantages.

All three methods are effective for electronic structure problems.

The paper discusses the similarities and differences among these techniques.

Abstract

A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.