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Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability

Please always quote using this URN:urn:nbn:de:0296-matheon-219
  • This paper is concerned with transparent boundary conditions (TBCs) for the time-dependent Schrödinger equation in one and two dimensions. Discrete TBCs are introduced in the numerical simulations of whole space problems in order to reduce the computational domain to a finite region. Since the discrete TBC for the Schrödinger equation includes a convolution w.r.t. time with a weakly decaying kernel, its numerical evaluation becomes very costly for large-time simulations. As a remedy we construct approximate TBCs with a kernel having the form of a finite sum-of-exponentials, which can be evaluated in a very efficient recursion. We prove stability of the resulting initialboundary value scheme, give error estimates for the considered approximation of the boundary condition, and illustrate the efficiency of the proposed method on several examples.

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Metadaten
Author:Anton Arnold, Matthias Ehrhardt, Ivan Sofronov
URN:urn:nbn:de:0296-matheon-219
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2003/12/17
Release Date:2003/12/17
Institute:Technische Universität Berlin
Preprint Number:13
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