A friendly review of absorbing boundary conditions and perfectly matched layers for classical and relativistic quantum waves equations

ABSTRACT

The aim of this paper is to describe concisely the recent theoretical and numerical developments concerningabsorbing boundary conditions and perfectly matched layers for solving classical and relativistic quantum waves problems. The equations considered in this paper are the Schrödinger, Klein–Gordon and Dirac equations.

KEYWORDS:

• Classical quantum waves
• relativistic quantum waves
• Schrödinger equation
• Klein–Gordon equation
• Dirac equation
• absorbing boundary conditions
• perfectly matched layers
• numerical schemes
• simulation

Acknowledgments

The authors warmly thank Professor Olivier Pinaud (Colorado State University) for discussions about PMLs for the Dirac equation and for providing the simulations from Figure 8.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

French ANR (Agence Nationale de la Recherche) grants [ANR-13-BS01-0009-01], [ANR-12-MONU-0007-02]; NSERC (Natural Sciences and Engineering Research Council of Canada [Grant no.: 315846]) via the Discovery Grant program.