Numerical Solution of Time-Dependent Nonlinear Schrödinger Equations Using Domain Truncation Techniques Coupled With Relaxation Scheme

Xavier Antoine (1, 2) , Christophe Besse (3, 4) , Pauline Klein (5)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECN - Institut Élie Cartan de Nancy
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 SIMPAF - SImulations and Modeling for PArticles and Fluids
5 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

The aim of this paper is to compare different ways for truncating unbounded domains for solving general nonlinear one- and two-dimensional Schrödinger equations. We propose to analyze Complex Absorbing Potentials, Perfectly Matched Layers and Absorbing Boundary Conditions. The time discretization is made by using a semi-implicit relaxation scheme which avoids any fixed point procedure. The spatial discretization involves finite element methods. We propose some numerical experiments to compare the approaches.

Mots clés: absorbing boundary conditions; complex absorbing potentials; nonlinear schrödinger equation; unbounded domain; perfectly matched layers; relaxation scheme

Domaines: Analyse numérique [math.NA]

Xavier Antoine, Christophe Besse, Pauline Klein. Numerical Solution of Time-Dependent Nonlinear Schrödinger Equations Using Domain Truncation Techniques Coupled With Relaxation Scheme. Laser Physics, 2011, 21 (8), pp.1-12. ⟨hal-00755612⟩