Open boundaries for the nonlinear Schrodinger equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:225

Article

Soffer, A.¹  Stucchio, C.¹ 

[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

关键词: absorbing boundary conditions;    spectral methods;    nonlinear Schrodinger equation;    harmonic analysis;    phase space localization;   

DOI  :  10.1016/j.jcp.2007.01.020

来源: Elsevier

【 摘 要 】

We present a new algorithm, the time dependent phase space filter (TDPSF) which is used to solve time dependent nonlinear Schrodinger equations (NLS). The algorithm consists of solving the NLS on a box with periodic boundary conditions (by any algorithm). Periodically in time we decompose the solution into a family of coherent states. Coherent states which are outgoing are deleted, while those which are not are kept, reducing the problem of reflected (wrapped) waves. Numerical results are given, and rigorous error estimates are described. The TDPSF is compatible with spectral methods for solving the interior problem. The TDPSF also fails gracefully, in the sense that the algorithm notifies the user when the result is incorrect. We are aware of no other method with this capability. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free