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Numerical solution of time-dependent nonlinear Schrodinger equations using domain truncation techniques coupled with

Summary: Numerical solution of time-dependent nonlinear Schr¨odinger
equations using domain truncation techniques coupled with
relaxation scheme
X. Antoinea,1,
, C. Besseb,1
, P. Kleina,1
Institut Elie Cartan Nancy, Nancy-Universit´e, CNRS UMR 7502, INRIA CORIDA Team, Boulevard des
Aiguillettes B.P. 239, 54506 Vandoeuvre-l`es-Nancy, France
Laboratoire Paul Painlev´e, Univ Lille Nord de France, CNRS UMR 8524, INRIA SIMPAF Team,
Universit´e Lille 1 Sciences et Technologies, Cit´e Scientifique, 59655 Villeneuve d'Ascq Cedex, France
The aim of this paper is to compare different ways for truncating unbounded domains for
solving general nonlinear one- and two-dimensional Schr¨odinger equations. We propose to
analyze Complex Absorbing Potentials, Perfectly Matched Layers and Absorbing Boundary
Conditions. The time discretization is made by using a semi-implicit relaxation scheme
which avoids any fixed point procedure. The spatial discretization involves finite element
methods. We propose some numerical experiments to compare the approaches.
Keywords: Complex Absorbing Potentials, Absorbing Boundary Conditions, Perfectly


Source: Antoine, Xavier - Institut de Mathématiques Élie Cartan, Université Henri Poincaré - Nancy 1


Collections: Mathematics