Perfectly matched layer for computing the dynamics of nonlinear Schrodinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates
Perfectly matched layer for computing the dynamics of nonlinear Schrodinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates
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DOI：
10.1016/j.cnsns.2020.105406
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发表时间：
2020-11-01
影响因子：
3.9
通讯作者：
Tang, Qinglin
中科院分区：
文献类型：
--
作者：
Antoine, Xavier;Geuzaine, Christophe;Tang, Qinglin
在本文中，我们首先提出了一种在用于模拟非线性薛定谔方程动力学的最标准数值方案中实现完美匹配层（PML）方法的通用策略。这些方法基于时间分割 Bao 等人。 (2003)[15]或时间上的松弛Besse(2004)[24]方案，以及空间上基于FFT的伪谱离散化方法。针对线性和非线性问题进行了彻底的数值研究，以了解 PML 方法对于给定方案的行为（吸收函数和调整参数）。然后，Antonelli 等人利用旋转拉格朗日坐标变换方法提出了旋转 Gross-Pitaevskii 方程的扩展。 (2012)，包等人。 (2013)，加西亚-里波尔等人。 (2001)[13,16,38]，一些数值模拟说明了所提出方法的优点。 (c) 2020 Elsevier B.V. 保留所有权利。
In this paper, we first propose a general strategy to implement the Perfectly Matched Layer (PML) approach in the most standard numerical schemes used for simulating the dynamics of nonlinear Schrodinger equations. The methods are based on the time-splitting Bao et al. (2003)[15] or relaxation Besse (2004)[24] schemes in time, and FFT-based pseudospectral discretization method in space. A thorough numerical study is developed for linear and nonlinear problems to understand how the PML approach behaves (absorbing function and tuning parameters) for a given scheme. The extension to the rotating Gross-Pitaevskii equation is then proposed by using the rotating Lagrangian coordinates transformation method Antonelli et al. (2012), Bao et al. (2013), Garcia-Ripoll et al. (2001)[13,16,38], some numerical simulations illustrating the strength of the proposed approach. (c) 2020 Elsevier B.V. All rights reserved.