The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schroedinger equation
- Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay (Hong Kong)
- Department of Mathematics, Michigan State University, East Lansing, MI 48824 (United States)
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . 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 compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.
- OSTI ID:
- 21418120
- Journal Information:
- Journal of Computational Physics, Vol. 229, Issue 23; Other Information: DOI: 10.1016/j.jcp.2010.08.015; PII: S0021-9991(10)00452-3; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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