An efficient split-step and implicit pure mesh-free method for the 2D/3D nonlinear Gross-Pitaevskii equations
An efficient split-step and implicit pure mesh-free method for the 2D/3D nonlinear Gross-Pitaevskii equations
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2D/3D非线性Gross-Pitaevskii方程的高效分步隐式纯无网格方法
DOI：
10.1016/j.cpc.2018.05.007
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发表时间：
2018
影响因子：
6.3
通讯作者：
Wang Deng Shan
中科院分区：
文献类型：
--
作者：
Jiang Tao;Chen Zhen Chao;Lu Wei Gang;Yuan Jin Yun;Wang Deng Shan
本文发展了一种高效的、分步的、隐式修正的并行光滑粒子流体动力学（SS-ICPSPH）方法，用于模拟多个非线性Schr dinger/Gross-Pitaevskii方程（NLSE/GPE）的动力学系统。所提出的方法是由分裂步骤的方程，传统的SPH和时间的隐式格式的修正对称核梯度，分别。同时，为了提高计算效率，引入了MPI并行技术.首先，通过求解二维非线性最小二乘方程，验证了该方法的数值精度和优越性，并与解析解进行了比较。其次，将新方法推广到二维/三维双分量GPE的数值模拟，并与高精度有限差分结果进行了比较。第三，将所提出的方法推广到研究旋转玻色-爱因斯坦凝聚体中的片状涡旋。最后，将隐式修正SPH格式推广到具有初始扰动的矩形池中自由表面波的传播过程。所有的数值结果表明了该方法的能力和可靠性。
In this paper, a high-efficient, split-step, and implicit corrected parallel smoothed particle hydrodynamics (SS-ICPSPH) method is developed to simulate the dynamic systems of several nonlinear Schrödinger/Gross–Pitaevskii equations (NLSE/GPE). The proposed method is motivated by the split-step for the equation, the corrected symmetric kernel gradient for the traditional SPH and the implicit scheme for time, respectively. Meanwhile, the MPI parallel technique is introduced to enhance the computational efficiency. Firstly, the numerical accuracy and the merits of the proposed method are tested by solving 2D NLSE, and compared with the analytical results. Secondly, the new method is extended to simulate the 2D/3D two-component GPE, compared with high accuracy finite difference results. Thirdly, the proposed method is extended to investigate the sheet-like vortices in rotating Bose–Einstein condensate. Finally, the implicit corrected SPH scheme is tentatively extended to capture the propagation process of free surface wave in a rectangular pool with initial perturbation. All the numerical results show the ability and the reliability of the proposed method.