Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. Part II: Discretization and numerical results

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

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECL - Institut Élie Cartan de Lorraine
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

Four families of ABCs where built in [5] for the two- dimensional linear Schr ̈odinger equation with time and space depen- dent potentials and for general smooth convex fictitious surfaces. The aim of this paper is to propose some suitable discretization schemes of these ABCs and to prove some semi-discrete stability results. Fur- thermore, the full numerical discretization of the corresponding initial boundary value problems is considered and simulations are provided to compare the accuracy of the different ABCs.

Domaines: Analyse numérique [math.NA]

Xavier Antoine, Christophe Besse, Pauline Klein. Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. Part II: Discretization and numerical results. Numerische Mathematik, 2013, 125 (2), pp.191-223. ⟨hal-00931115⟩