Title :

A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations

Author(s) :

Antoine, Xavier [Auteur]
Institut Élie Cartan de Nancy [IECN]
Robust control of infinite dimensional systems and applications [CORIDA]
Arnold, Anton [Auteur]
Institut für Numerische und Angewandte Mathematik
Besse, Christophe [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Ehrhardt, Matthias [Auteur]
Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] [WIAS]
Schädle, Achim [Auteur]
Zuse Institute Berlin [ZIB]

Journal title :

Communications in Computational Physics

Pages :

729-796

Publisher :

Global Science Press

Publication date :

2008

ISSN :

1815-2406

HAL domain(s) :

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

English abstract : [en]

In this review article we discuss different techniques to solve numerically the time-dependent Schrödinger equation on unbounded domains. We present and compare several approaches to implement the classical transparent ...
Show more >In this review article we discuss different techniques to solve numerically the time-dependent Schrödinger equation on unbounded domains. We present and compare several approaches to implement the classical transparent boundary condition into finite difference and finite element discretizations. We present in detail the approaches of the authors and describe briefly alternative ideas pointing out the relations between these works. We conclude with several numerical examples from different application areas to compare the presented techniques. We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL