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

Xavier Antoine (1, 2) , Emmanuel Lorin (3, 4) , Qinglin Tang (5, 2)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine
3 CRM - Centre de Recherches Mathématiques [Montréal]
4 School of Mathematics and Statistics [Ottawa]
5 LMRS - Laboratoire de Mathématiques Raphaël Salem

The aim of this paper is to describe concisely the recent theoretical and numerical developments concerning absorbing 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.

Mots clés: classical quantum waves; numerical schemes; simulation; absorbing boundary conditions; relativistic quantum waves; perfectly matched layers; Dirac equation; Klein-Gordon equation; Schrödinger equation

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Chimie théorique et/ou physique; Modélisation et simulation; Physique Quantique [quant-ph]

Xavier Antoine, Emmanuel Lorin, Qinglin Tang. A friendly review of absorbing boundary conditions and perfectly matched layers for classical and relativistic quantum waves equations. Molecular Physics, 2017, 115 (15-16), pp.1861-1879. ⟨10.1080/00268976.2017.1290834⟩. ⟨hal-01374183⟩