Frozen Gaussian approximation based domain decomposition methods for the linear Schrodinger equation beyond the semi-classical regime

JOURNAL OF COMPUTATIONAL PHYSICS

卷:315

Article

Lorin, E.^1,2  Yang, X.³  Antoine, X.⁴ 

[1] Univ Montreal, Ctr Rech Math, Montreal, PQ H3T 1J4, Canada

[2] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada

[3] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

[4] Univ Lorraine, Inria Nancy Grand Est, Inst Elie Cartan Lorraine, F-54506 Vandoeuvre Les Nancy, France

关键词: Semiclassical approximation;    Absorbing boundary condition;    Domain decomposition;    Linear Schrodinger equation;    Pseudodifferential operators;   

DOI  :  10.1016/j.jcp.2016.02.035

来源: Elsevier

【 摘 要 】

The paper is devoted to develop efficient domain decomposition methods for the linear Schrodinger equation beyond the semiclassical regime, which does not carry a small enough rescaled Planck constant for asymptotic methods (e.g. geometric optics) to produce a good accuracy, but which is too computationally expensive if direct methods (e.g. finite difference) are applied. This belongs to the category of computing middle-frequency wave propagation, where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy. Motivated by recent works of the authors on absorbing boundary conditions (Antoine et al. (2014) [13] and Yang and Zhang (2014) [43]), we introduce Semiclassical Schwarz Waveform Relaxation methods (SSWR), which are seamless integrations of semiclassical approximation to Schwarz Waveform Relaxation methods. Two versions are proposed respectively based on Herman-Kluk propagation and geometric optics, and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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