Spurious Modes in Dirac Calculations and How to Avoid Them

TL;DR

This paper investigates the problem of spurious modes in Dirac operator eigenvalue calculations, providing mathematical insights, numerical experiments, and discussing unresolved issues to improve computational accuracy.

Contribution

It introduces recent mathematical results on spurious modes in Dirac eigenvalue computations and illustrates them with numerical experiments, highlighting open problems.

Findings

Identification of conditions leading to spurious modes

Numerical experiments demonstrating the occurrence of spurious modes

Discussion of open problems in avoiding spurious solutions

Abstract

In this paper we consider the problem of the occurrence of spurious modes when computing the eigenvalues of Dirac operators, with the motivation to describe relativistic electrons in an atom or a molecule. We present recent mathematical results which we illustrate by simple numerical experiments. We also discuss open problems.