In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation in three dimensions. Based on the idea of the scalar auxiliary variable approach which is proposed in the recent papers [J. Comput. Phys., 416 (2018) 353-407 and SIAM Rev., 61(2019) 474-506] for developing energy stable schemes for gradient flow systems, we firstly reformulate the Gross-Pitaevskii equation into an equivalent system with a modified energy conservation law. The reformulated system is then discretized by the Gauss collocation method in time and the standard Fourier pseudo-spectral method in space, respectively. We show that the proposed schemes can preserve the discrete mass and modified energy exactly. Numerical results are addressed to verify the efficiency and high-order accuracy of the proposed schemes.

中文翻译：

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具有角动量旋转的 Gross-Pitaevskii 方程的任意高阶结构保持方案

在本文中，我们为具有三维角动量旋转的瞬态 Gross-Pitaevskii 方程设计了一类新的任意高阶结构保持数值方案。基于最近论文中提出的标量辅助变量方法的思想[J. 计算。Phys., 416 (2018) 353-407 and SIAM Rev., 61(2019) 474-506] 用于开发梯度流系统的能量稳定方案，我们首先将 Gross-Pitaevskii 方程重新表述为具有修正能量守恒的等效系统法律。然后分别通过时间上的高斯配置方法和空间上的标准傅立叶伪谱方法对重新制定的系统进行离散化。我们表明，所提出的方案可以准确地保留离散质量和修改后的能量。