A family of new explicit, revertible, volume-preserving numerical schemes for the system of Lorentz force

Tu, Xiongbiao; Zhu, Beibei; Tang, Yifa; Qin, Hong; Liu, Jian; Zhang, Ruili

doi:10.1063/1.4972878

Cited by 13 publications

(10 citation statements)

References 18 publications

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“…) is symplectic and integrator ψ m is variational symplectic. Further, substituting the relation of p = ∂L/∂ ẋ = v + (−ωy, ωx, 0), one can easily compute the map of (v n , x n ) → (v n+1 , x n+1 ) (refer to the formula (6) in Tu et al (2016)), which is a K-symplectic integrator. So the ψ m also implies a K-symplectic integrator…”

Section: The Symplectic Property -The Implicit Midpoint Scheme ψ Mmentioning

confidence: 99%

Symplectic Integrators in Corotating Coordinates

Tu¹,

Wang²,

Tang³

2022

Preprint

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The dynamic equation of mass point in rotating coordinates is governed by Coriolis and centrifugal force, besides a corotating potential relative to frame. Such a system is no longer a canonical Hamiltonian system so that the construction of symplectic integrator is problematic. In this paper, we present three integrators for this question. It is significant that those schemes have the good property of near-conservation of energy. We proved that the discrete symplectic map of (p n , x n ) → (p n+1 , x n+1 ) in corotating coordinates exists and the two integrators are variational symplectic. Two groups of numerical experiments demonstrates the precision and long-term convergence of these integrators in the examples of corotating top-hat density and circular restricted three-body system.

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Section: The Symplectic Property -The Implicit Midpoint Scheme ψ Mmentioning

confidence: 99%

Symplectic Integrators in Corotating Coordinates

Tu¹,

Wang²,

Tang³

2022

Preprint

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“…The Hamiltonian system is an important category of dynamical systems, which can represent all real physical processes with negligible dissipation. It has a very wide range of applications, such as biology [1], plasma physics [2][3][4][5] and celestial mechanics [6,7]. The basis of Hamiltonian system is symplectic geometry which is the phase space composed of n generalized coordinates and n generalized momentum in a system with n degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Symplectic All-at-Once Method for Hamiltonian Systems

Zhu

Zhao

2021

Symmetry

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The all-at-once technique has attracted many researchers’ interest in recent years. In this paper, we combine this technique with a classical symplectic and symmetric method for solving Hamiltonian systems. The solutions at all time steps are obtained at one-shot. In order to reduce the computational cost of solving the all-at-once system, a fast algorithm is designed. Numerical experiments of Hamiltonian systems with degrees of freedom n≤3 are provided to show that our method is more efficient than the classical symplectic method.

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“…According to theoretical and numerical investigations, numerical errors of symplectic integrators on invariants of the systems, such as the total energy and momentum, can be bounded by small numbers for all time-steps [47,55,56,60]. In plasma physics, many fundamental models are canonical or non-canonical cently developed, including those for guiding centers [61][62][63][64][65][66][67][68], charged particles [44,[69][70][71][72][73][74][75][76][77][78][79],…”

Section: Introductionmentioning

confidence: 99%

Field theory and a structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence

Xiao

Qin

2019

Nucl. Fusion

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A field theory and the associated structure-preserving geometric Particle-In-Cell (PIC) algorithm are developed to study low frequency electrostatic perturbations with fully kinetic ions and adiabatic electrons in magnetized plasmas. The algorithm is constructed by geometrically discretizing the field theory using discrete exterior calculus, high-order Whitney interpolation forms, and non-canonical Hamiltonian splitting method. The discretization preserves the non-canonical symplectic structure of the particle-field system, as well as the electromagnetic gauge symmetry.As a result, the algorithm is charge-conserving and possesses long-term conservation properties.Because drift wave turbulence and anomalous transport intrinsically involve multi time-scales, simulation studies using fully kinetic particle demand algorithms with long-term accuracy and fidelity.The structure-preserving geometric PIC algorithm developed adequately servers this purpose. The algorithm has been implemented in the SymPIC code, tested and benchmarked using the examples of ion Bernstein waves and drift waves. We apply the algorithm to study the Ion Temperature Gradient (ITG) instability and turbulence in a 2D slab geometry. Simulation results show that at the early stage of the turbulence, the energy diffusion is between the Bohm scaling and gyro-Bohm scaling. At later time, the observed diffusion is closer to the gyro-Bohm scaling, and density blobs generated by the rupture of unstable modes are the prominent structures of the fully developed ITG turbulence. * hongqin@princeton.edu

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A family of new explicit, revertible, volume-preserving numerical schemes for the system of Lorentz force

Cited by 13 publications

References 18 publications

Symplectic Integrators in Corotating Coordinates

Symplectic Integrators in Corotating Coordinates

Symplectic All-at-Once Method for Hamiltonian Systems

Field theory and a structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence

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