Absorbing Boundary Conditions for the Two-Dimensional Schrödinger Equation with an Exterior Potential. Part II: Discretization and Numerical ResultsReport as inadecuate




Absorbing Boundary Conditions for the Two-Dimensional Schrödinger Equation with an Exterior Potential. Part II: Discretization and Numerical Results - Download this document for free, or read online. Document in PDF available to download.

1 EDP - Equations aux dérivées partielles IECL - Institut Élie Cartan de Lorraine 2 CORIDA - Robust control of infinite dimensional systems and applications IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est 3 LPP - Laboratoire Paul Painlevé 4 LMB - Laboratoire de Mathématiques de Besançon

Abstract : Four families of ABCs where built in 5 for the two- dimensional linear Schr ̈odinger equation with time and space depen- dent potentials and for general smooth convex fictitious surfaces. The aim of this paper is to propose some suitable discretization schemes of these ABCs and to prove some semi-discrete stability results. Fur- thermore, the full numerical discretization of the corresponding initial boundary value problems is considered and simulations are provided to compare the accuracy of the different ABCs.





Author: Xavier Antoine - Christophe Besse - Pauline Klein -

Source: https://hal.archives-ouvertes.fr/



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