Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and NonlinearitiesReportar como inadecuado




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1 LMB - Laboratoire de Mathématiques de Besançon 2 IECN - Institut Élie Cartan de Nancy 3 EDP - Equations aux dérivées partielles IECL - Institut Élie Cartan de Lorraine 4 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 5 LPP - Laboratoire Paul Painlevé 6 SIMPAF - SImulations and Modeling for PArticles and Fluids LPP - Laboratoire Paul Painlevé, Inria Lille - Nord Europe 7 Institut für Numerische und Angewandte Mathematik

Abstract : We propose a hierarchy of novel absorbing boundary conditions for the one-dimensional stationary Schrö\-din\-ger 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 Schrödinger 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 Schrödinger equations.





Autor: Pauline Klein - Xavier Antoine - Christophe Besse - Matthias Ehrhardt -

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



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