论文标题
在三个维度上旋转角度动量旋转的Gross-pitaevskii方程的任意高阶结构赋予方案
Arbitrarily high-order structure-preserving schemes for the Gross-Pitaevskii equation with angular momentum rotation in three dimensions
论文作者
论文摘要
在本文中，我们为时间依赖性的Gross-Pitaevskii方程设计了一类新的高阶结构保留数值方案，并在三个维度中具有角动量旋转。基于在最近的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和Siam Rev.，61（2019）474-506]用于开发用于梯度流量系统的能量稳定方案，我们首先将Gross-Pitaevskii方程式重新制定为具有改良的能量保护法的高度Pitaevskii方程。然后，随时间和空间中的标准傅立叶伪谱法分别通过高斯配置法离散重新制定的系统。我们表明，所提出的方案可以保留离散的质量和修改能量。确定了数值结果以验证所提出方案的效率和高阶精度。
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.
