Paper Info
Title
An efficient split-step and implicit pure mesh-free method for the 2D/3D nonlinear Gross-Pitaevskii equations.
Abstract
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.
Year
DOI
Venue
2018
10.1016/j.cpc.2018.05.007
Computer Physics Communications
Keywords
Field
DocType
SPH,Nonlinear Schrödinger equation,Bose–Einstein condensates,Parallelization,Propagation of free surface wave
Kernel (linear algebra),Smoothed-particle hydrodynamics,Free surface,Nonlinear system,Finite difference,Mathematical analysis,Vortex,Dynamical system,Perturbation (astronomy),Mathematics
Journal
Volume
ISSN
Citations 
231
0010-4655
0
PageRank 
References 
Authors
0.34
16
5
Name
Order
Citations
PageRank
Tao Jiang100.34
Zhengchao Chen22210.85
Wei-Gang Lu300.34
Jin-Yun Yuan400.34
Deng-Shan Wang59219.07