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Schwarz waveform relaxation method for one-dimensional Schrödinger equation with general potential

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Abstract

In this paper, we apply the Schwarz waveform relaxation (SWR) method to the one-dimensional Schrödinger equation with a general linear or a nonlinear potential. We propose a new algorithm for the Schrödinger equation with time-independent linear potential, which is robust and scalable up to 500 subdomains. It reduces significantly computation time compared with the classical algorithms. Concerning the case of time-dependent linear potential or the nonlinear potential, we use a preprocessed linear operator for the zero potential case as a preconditioner which leads to a preconditioned algorithm. This ensures high scalability. In addition, some newly constructed absorbing boundary conditions are used as the transmission conditions and compared numerically.

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Author notes

  1. Feng Xing

    Present address: Laboratoire J.A. Dieudonné, Université de Nice & Inria Sophia Antipolis, Nice, France

Authors and Affiliations

  1. Institut de Mathématiques de Toulouse UMR5219, Université de Toulouse, CNRS, UPS IMT, 31062, Toulouse Cedex 9, France

    Christophe Besse

  2. Maison de la Simulation & Laboratoire Paul Painlevé, Université Lille Nord de France, Lille, France

    Feng Xing

Authors
  1. Christophe Besse
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  2. Feng Xing
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Correspondence to Feng Xing.

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Besse, C., Xing, F. Schwarz waveform relaxation method for one-dimensional Schrödinger equation with general potential. Numer Algor 74, 393–426 (2017). https://doi.org/10.1007/s11075-016-0153-4

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  • DOI: https://doi.org/10.1007/s11075-016-0153-4

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