Title :

Absorbing Boundary Conditions for the Two-Dimensional Schrödinger Equation with an Exterior Potential. Part I: Construction and a priori Estimates

Author(s) :

Antoine, Xavier [Auteur]
Robust control of infinite dimensional systems and applications [CORIDA]
Institut Élie Cartan de Nancy [IECN]
Besse, Christophe [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Klein, Pauline [Auteur]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]

Journal title :

Mathematical Models and Methods in Applied Sciences

Pages :

1250025

Publisher :

World Scientific Publishing

Publication date :

2012

ISSN :

0218-2025

English keyword(s) :

variable potential
absorbing boundary conditions
Schrödinger equation

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Mathématiques générales [math.GM]

English abstract : [en]

The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. ...
Show more >The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, \textit{a priori} estimates are developed for the truncated problems with various increasing order boundary conditions. The effective numerical approximation will be treated in a second paper.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL