Commun. Comput. Phys., 10 (2011), pp. 1280-1304.


Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrodinger Equations with Unbounded Potentials and Nonlinearities

Pauline Klein 1, Xavier Antoine 1*, Christophe Besse 2, Matthias Ehrhardt 3

1 Institut Elie Cartan Nancy, Nancy-Universite, CNRS UMR 7502, INRIA CORIDA Team, Boulevard des Aiguillettes B.P. 239, 54506 Vandoeuvre-les-Nancy, France.
2 Laboratoire Paul Painleve, CNRS UMR 8524, Simpaf Project Team-Inria CR Lille Nord Europe, Universite des Sciences et Technologies de Lille, Cite Scientifique, 59655 Villeneuve d'Ascq Cedex, France.
3 Lehrstuhl fur Angewandte Mathematik und Numerische Analysis, Fachbereich C-Mathematik und Naturwissenschaften, Bergische Universitat Wuppertal, Gaussstr. 20, 42119 Wuppertal, Germany.

Received 25 October 2010; Accepted (in revised version) 16 February 2011
Available online 2 August 2011
doi:10.4208/cicp.251010.160211a

Abstract

We propose a hierarchy of novel absorbing boundary conditions for the one-dimensional stationary Schrodinger equation with general (linear and nonlinear) potential. The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schrodinger equations. It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition. Finally, we give the extension of these ABCs to N-dimensional stationary Schrodinger equations.

AMS subject classifications: 35J10, 65M60, 65N30

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Key words: Absorbing boundary conditions, stationary Schrodinger equations, unbounded domain, spatially dependent potential, ground states computation.

*Corresponding author.
Email: pauline.klein@iecn.u-nancy.fr (P. Klein), xavier.antoine@iecn.u-nancy.fr (X. Antoine), christophe.besse@math.univ-lille1.fr (C. Besse), ehrhardt@math.uni-wuppertal.de (M. Ehrhardt)
 

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