Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrodinger/Gross-Pitaevskii equations
Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrodinger/Gross-Pitaevskii equations
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DOI：
10.1016/j.jcp.2021.110328
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发表时间：
2021-04-09
影响因子：
4.1
通讯作者：
Tang, Qinglin
中科院分区：
文献类型：
--
作者：
Antoine, Xavier;Shen, Jie;Tang, Qinglin
本文基于标量辅助变量（SAV）方法[44，45]和新近提出的用于梯度流的拉格朗日乘子（LagM）方法[22，21]，提出了两种模拟一般非线性Schrodinger/Gross-Pitaevskii方程动力学的线性隐式伪谱格式。这两种方案在空间/时间方向上具有谱/二阶精度。基于SAV的方案保留了修改后的总能量，并将质量近似为三阶（相对于时间步长），而基于LagM的方案可以精确地保留质量和原始总能量。基于LagM的格式在每一个时间步都需要求解一个非线性代数方程组，因此SAV格式通常比LagM格式更有效。另一方面，LagM格式可能优于SAV格式，因为它保持了原始的总能量和质量，并且通常允许较小的误差。大量的数值结果表明，所提出的计划的有效性，精度和性能。(c)2021爱思唯尔公司All rights reserved.
In this paper, based on the Scalar Auxiliary Variable (SAV) approach [44,45] and a newly proposed Lagrange multiplier (LagM) approach [22,21] originally constructed for gradient flows, we propose two linear implicit pseudo-spectral schemes for simulating the dynamics of general nonlinear Schrodinger/Gross-Pitaevskii equations. Both schemes are of spectral/second-order accuracy in spatial/temporal direction. The SAV based scheme preserves a modified total energy and approximate the mass to third order (with respect to time steps), while the LagM based scheme could preserve exactly the mass and original total energy. A nonlinear algebraic system has to be solved at every time step ford the LagM based scheme, hence the SAV scheme is usually more efficient than the LagM one. On the other hand, the LagM scheme may outperform the SAV ones in the sense that it conserves the original total energy and mass and usually admits smaller errors. Ample numerical results are presented to show the effectiveness, accuracy and performance of the proposed schemes. (c) 2021 Elsevier Inc. All rights reserved.