三维角动量旋转Gross-Pitaevskii方程的高阶保结构格式
Arbitrarily high-order structure-preserving schemes for the Gross-Pitaevskii equation with angular momentum rotation in three dimensions
摘要：
本文针对三维含时Gross-Pitaevskii方程，设计了一类新的任意高阶保结构数值格式.本文基于近年来提出的标量辅助变量法的思想[J. Comput.物理、416（2018）353-407和SIAM Rev.，61（2019）474-506]为了开发梯度流系统的能量稳定格式，我们首先将Gross-Pitaevskii方程重新表示为具有修改的能量守恒律的等效系统。在时间上用高斯配置法离散，在空间上用标准傅立叶准谱方法离散。我们证明了所提出的格式可以精确地保持离散质量和修正能量。数值结果验证了所提出的格式的效率和高阶精度。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
