An efficient split-step and implicit pure mesh-free method for the 2D/3D nonlinear Gross–Pitaevskii equations

Jiang, Tao; Chen, Zhengchao; Lü, Wenpeng; Yuan, Jinyun; Wang, Deng‐Shan

doi:10.1016/j.cpc.2018.05.007

Cited by 24 publications

(14 citation statements)

References 48 publications

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“…This data smoothing method is commonly used to infer populations from a finite data sample. It has also been used in grid-free simulations of the GPE, which is of particular relevance here [46,47]. The kernel density estimator for M samples is given by…”

Section: B Boltzmann-vlasov Equation Simulationmentioning

confidence: 99%

Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

et al. 2018

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The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective 1D Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matterwave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the classical simulation, suggesting that observing such an exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the non-interacting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms. arXiv:1808.07196v2 [quant-ph]

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Section: B Boltzmann-vlasov Equation Simulationmentioning

confidence: 99%

Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

et al. 2018

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“…The flow field contains strong discontinuity surfaces such as moving boundaries, shock wave, and combustion wave, etc., the deformed meshes near the moving boundaries need to be reconstructed, and the judgment of intersection and penetration among points, lines and surfaces in the reconstruction process is extremely complicated. Traditional CFD methods are mostly based on meshes, but the existence of meshes has limited the application of these methods in solving flow fields with complex boundaries [15][16][17][18][19][20]. Therefore, the method that can perform numerical analysis on flow problems without the necessity of meshing has become a research hotspot and the mesh-less method [21][22][23][24][25][26][27] has been applied to the study of fluid mechanics ever since.…”

Section: Introductionmentioning

confidence: 99%

Application of Three-Dimensional Meshless Method in Muzzle Flow Field of Projectile with Large Displacement

Wang¹,

Xue²,

Cai³

et al. 2021

IJHT

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The mesh-less method abandons the idea of traditional mesh method. In numerical calculation, it only needs the node information, and it's not necessary to connect nodes into mesh cells. Aiming at the problem of non-equilibrium chemical reaction flows in a threedimensional muzzle with moving boundaries, this paper proposed a three-dimensional least squares mesh-less (3D-LSM) algorithm, and the ALE (Arbitrary Lagrangian-Eulerian) form multi-component Euler governing equations were adopted for fluid dynamics modeling; then, a finite-rate reaction model was used to deal with the chemical reactions in the flow field, a time-division method was applied to solve the stiff problem of chemical reactions, and multi-component AUFS (artificially upstream flux vector splitting) format was introduced to calculate the convective flux term of the governing equation. In addition, the weighted-point filling strategy and the dynamic point cloud method were employed to deal with the topological structure changes in the point clouds caused by the large displacement movement of the projectile in the three-dimensional muzzle flow field. Finally, the proposed mesh-less method was applied to calculate the muzzle of a 12.7mm gun, and accurately captured the bottle-shaped shock wave structure in the complex muzzle flow field and the second muzzle flame phenomenon; the calculation results were compared with the experimental results and obtained a good match, which had proved the feasibility of the proposed 3D-LSM method. The research findings of this paper provided a new solution for the simulation of high-speed non-equilibrium reaction jets with multicomponent and large-displacement moving boundaries.

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“…The nonlinear Schrödinger equation (NLSE) is truly a universal equation as it describes major fields such as Bose-Eienstein condensation [1], nonlinear optics [2], ocean waves [3], and many others [4][5][6]. This has stimulated extensive interest in its analytical [7] and numerical solutions [8][9][10][12][13][14][15][16][17][18][19]. Over decades, knowledge about its analytical solutions has accumulated such that it is now rare to find a new solution [7].…”

Section: Introductionmentioning

confidence: 99%

High accuracy power series method for solving scalar, vector, and inhomogeneous nonlinear Schrödinger equations

Sakkaf¹,

Khawaja²

2021

Preprint

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We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schrödinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of magnitude larger than those of other methods. Machine precision accuracy can be easily reached and sustained for long evolution times within rather short computing time. In-depth analysis and characterisation for all sources of error are performed by comparing the numerical solutions with the exact analytical ones. Exact and approximate boundary conditions are considered and shown to minimise errors for solutions with finite background. The method is extended to cases with external potentials and coupled nonlinear Schrödinger equations.

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An efficient split-step and implicit pure mesh-free method for the 2D/3D nonlinear Gross–Pitaevskii equations

Cited by 24 publications

References 48 publications

Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier

Application of Three-Dimensional Meshless Method in Muzzle Flow Field of Projectile with Large Displacement

High accuracy power series method for solving scalar, vector, and inhomogeneous nonlinear Schrödinger equations

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