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首页> 外文期刊>Journal of Computational Physics >Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrodinger/Gross-Pitaevskii equations
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Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrodinger/Gross-Pitaevskii equations

机译：基于标量辅助变量/拉格朗日乘法器的非线性施罗格/ GITOEVSKII方程的动态示例

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摘要

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.
机译：本文在标量辅助变量（SAV）方法[44,45]和新提出的拉格朗日乘子（LagM）方法[22,21]的基础上，提出了两种用于模拟一般非线性薛定谔/格罗斯-皮塔耶夫斯基方程动力学的线性隐式伪谱格式。两种方案在空间/时间方向上都具有光谱/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格式的非线性代数系统在每一个时间步都需要求解，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，因为它保存了原始的总能量和质量，并且通常允许较小的误差。文中给出了大量的数值结果，证明了所提方法的有效性、准确性和性能。（c）2021爱思唯尔公司保留所有权利。

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