Title :

Schwarz waveform relaxation method for one dimensional Schrödinger equation with general potential

Author(s) :

Besse, Christophe [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Xing, Feng [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Maison de la Simulation [MDLS]

Journal title :

Numerical Algorithms

Pages :

393-426

Publisher :

Springer Verlag

Publication date :

2017-02

ISSN :

1017-1398

English keyword(s) :

Absorbing boundary conditions
Schwarz Waveform Relaxation method
Schrödinger equation
Parallel algorithms

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

In this paper, we apply the Schwarz Waveform Relaxation (SWR) method to the one dimensional Schrödinger equation with a general linear or a nonlinear potential. We propose a new algorithm for the Schrödinger equation with ...
Show more >In this paper, we apply the Schwarz Waveform Relaxation (SWR) method to the one dimensional Schrödinger equation with a general linear or a nonlinear potential. We propose a new algorithm for the Schrödinger equation with time independent linear potential, which is robust and scalable up to 500 subdo-mains. It reduces significantly computation time compared with the classical algorithms. Concerning the case of time dependent linear potential or the non-linear potential, we use a preprocessed linear operator for the zero potential case as preconditioner which lead to a preconditioned algorithm. This ensures high scalability. Besides, some newly constructed absorbing boundary conditions are used as the transmission condition and compared numerically.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Simulation numérique avancée pour les condensats de Bose-Einstein : Modèles numériques déterministes et stochastiques, Calcul haute performance, Simulation d'expériences physiques

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL