ABSORBING BOUNDARY CONDITIONS FOR THE TWO-DIMENSIONAL SCHRÖDINGER EQUATION WITH AN EXTERIOR POTENTIAL PART I: CONSTRUCTION AND A PRIORI ESTIMATES-Reference-Cited by-同舟云学术

ABSORBING BOUNDARY CONDITIONS FOR THE TWO-DIMENSIONAL SCHRÖDINGER EQUATION WITH AN EXTERIOR POTENTIAL PART I: CONSTRUCTION AND A PRIORI ESTIMATES

Published:2012-08-13 Issue:10 Volume:22 Page:1250026
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

ANTOINE XAVIER¹,BESSE CHRISTOPHE²,KLEIN PAULINE³

Affiliation:

1. Institut Elie Cartan Nancy, Nancy-Université, CNRS UMR 7502, INRIA CORIDA Team, Boulevard des Aiguillettes B.P. 239, F-54506, Vandoeuvre-lès-Nancy, France

2. Laboratoire Paul Painlevé, Université Lille Nord de France, CNRS UMR 8524, INRIA SIMPAF Team, Université Lille 1 Sciences et Technologies, Cité Scientifique, 59655 Villeneuve d'Ascq Cedex, France

3. Laboratoire de Mathématiques de Besançon, CNRS UMR 6623, Université de Franche-Comté, 16 Route de Gray, 25030 Besançon, France

Abstract

The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, a priori estimates are developed for the truncated problems with various increasing order boundary conditions. The effective numerical approximation will be treated in a second paper.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202512500261

Reference28 articles.

1. Bayliss–Turkel-like Radiation Conditions on Surfaces of Arbitrary Shape

2. Construction, structure and asymptotic approximations of a microdifferential transparent boundary condition for the linear Schrödinger equation

3. Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation

4. Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential

Cited by 25 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Nonreflecting Boundary Condition for the Free Schrödinger Equation in 2D;2023 Photonics & Electromagnetics Research Symposium (PIERS);2023-07-03

2. Numerical study of the logarithmic Schrödinger equation with repulsive harmonic potential;Discrete and Continuous Dynamical Systems - B;2023

3. Introduction;Time Dependent Phase Space Filters;2023

4. Double-Preconditioning Techniques for Fractional Partial Differential Equation Solvers;Multiscale Science and Engineering;2022-09

5. A numerical study of fractional linear algebraic systems;Mathematics and Computers in Simulation;2021-04