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

Xavier Antoine; Anton Arnold; Christophe Besse; Matthias Ehrhardt; Achim Schädle

hal-00347884, version 1

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

Xavier Antoine () ^1, 2, Anton Arnold ³, Christophe Besse ^4, 5, Matthias Ehrhardt, Achim Schädle

Communications in Computational Physics 4, 4 (2008) 729-796

Abstract: 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.

1: Institut Elie Cartan Nancy (IECN)
CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
2: CORIDA (INRIA Nancy - Grand Est / IECN / LMAM)
INRIA – CNRS : UMR7502 – Université de Lorraine
3: Institut für Numerische und Angewandte Mathematik
Universität Münster
4: Laboratoire Paul Painlevé (LPP)
CNRS : UMR8524 – Université Lille I - Sciences et technologies
5: SIMPAF (INRIA Futurs)
INRIA

hal-00347884, version 1
http://hal.archives-ouvertes.fr/hal-00347884
oai:hal.archives-ouvertes.fr:hal-00347884
From: Xavier Antoine <>
Submitted on: Wednesday, 17 December 2008 09:24:53
Updated on: Friday, 19 December 2008 11:33:18

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