The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrdinger equation

Shing-Yu Leung Jianliang Qian

General Mathematics mathscidoc:1912.43184

Journal of Computational Physics, 229, (23), 8888-8917, 2010.11
We propose the backward phase flow method to implement the FourierBrosIagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrdinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to
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@inproceedings{shing-yu2010the,
  title={The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrdinger equation},
  author={Shing-Yu Leung, and Jianliang Qian},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112814517422744},
  booktitle={Journal of Computational Physics},
  volume={229},
  number={23},
  pages={8888-8917},
  year={2010},
}
Shing-Yu Leung, and Jianliang Qian. The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrdinger equation. 2010. Vol. 229. In Journal of Computational Physics. pp.8888-8917. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112814517422744.
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