Applying explicit symplectic-like methods to nonconservative nonseparable systems

Luo, Junjie; Wu, Xiaoxia

doi:10.1140/epjp/i2017-11765-4

Cited by 9 publications

(4 citation statements)

References 19 publications

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“…In particular, one of the advantages for the midpoint permutations lies in that the usual symplectic integration formulae can be directly applied to the extended phase space Hamiltonian but the methods of Pihajoki [31] and Liu et al [32] can not. These extended phase space explicit symmetric integrators have been shown to have good performance in the conservation of the original Hamiltonian when they are used to solve some inseparable Hamiltonian problems [3,34,35,43]. Now let us consider the application of an extended phase space fourth-order explicit symmetric algorithm with the midpoint permutations to the inseparable Hamiltonian (22).…”

Section: Investigations Of Orbital Dynamicsmentioning

confidence: 99%

Chaotic motion of neutral and charged particles in a magnetized Ernst-Schwarzschild spacetime

2019

Eur. Phys. J. Plus

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Neutral test particles around a Schwarzschild black hole immersed in an external uniform magnetic field have no interactions of electromagnetic forces, but their motions can be chaotic. This chaotic behavior is induced owing to the gravitational effect of the magnetic field leading to the nonintegrability of the magnetized Ernst-Schwarzschild spacetime geometry. In fact, chaos is strengthened typically with an increase of the energy or the magnetic field under appropriate circumstances. When these test particles have charges, the electromagnetic forces are included. As a result, the electromagnetic forces have an effect on strengthening or weakening the extent of chaos caused by the gravitational effect of the magnetic field.PACS numbers:

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Section: Investigations Of Orbital Dynamicsmentioning

confidence: 99%

Chaotic motion of neutral and charged particles in a magnetized Ernst-Schwarzschild spacetime

2019

Eur. Phys. J. Plus

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“…Liu et al [52] showed that sequent permutations of coordinates and momenta are a good choice of the mixing maps. Luo et al [53] found that midpoint permutations between coordinates and those between momenta are the best choice of the mixing maps. The midpoint permutation map is described by…”

Section: B Construction Of Symplectic-like Integrators In Extended Ph...mentioning

confidence: 99%

“…( 49) and ( 51), then f SO has 3PN spin-spin coupling and 3.5PN spin-orbit interaction. Thus, besides the terms in the approximate equations (52), many other terms such as the 2.5PN spin-orbit coupling and the 3PN spin-spin contribution are included in the exact equations (53). The 2.5PN spin-orbit and 3PN spin-spin contributions are implicitly hidden in the exact equations, but are absent in the approximate equations.…”

Section: A Dynamical Equationsmentioning

confidence: 99%

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Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations

Pan,

Wu,

Liang

2021

Preprint

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Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy and angular momentum. Doubling the phase-space variables of positions and momenta in the coherent equations, we establish extended phase-space symplectic-like integrators with the midpoint permutations. The velocities should be solved iteratively from the algebraic equations of the momenta defined by the Lagrangian during the course of numerical integrations. It is shown numerically that a fourthorder extended phase-space symplectic-like method exhibits good long-term stable error behavior in energy and angular momentum, as a fourth-order implicit symplectic method with a symmetric composition of three second-order implicit midpoint rules or a fourth-order Gauss-Runge-Kutta implicit symplectic scheme does. For given time step and integration time, the former method is superior to the latter integrators in computational efficiency. The extended phase-space method is used to study the effects of the parameters and initial conditions on the orbital dynamics of the coherent Euler-Lagrange equations for a post-Newtonian circular restricted three-body problem. It is also applied to trace the effects of the initial spin angles, initial separation and initial orbital eccentricity on the dynamics of the coherent post-Newtonian Euler-Lagrange equations of spinning compact binaries.

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GPU accelerated manifold correction method for spinning compact binaries

Song

Zhong

2018

Astrophys Space Sci

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The conservative Post-Newtonian (PN) Hamiltonian formulation of spinning compact binaries has six integrals of motion including the total energy, the total angular momentum and the constant unit lengths of spins. The manifold correction method can effectively eliminate the integration errors accumulation in a long time. In this paper, the accelerated manifold correction method based on graphics processing unit (GPU) is designed to simulate the dynamic evolution of spinning compact binaries. The feasibility and the efficiency of parallel computation on GPU for spinning compact binaries have been confirmed by various numerical experiments. The numerical comparisons show that the accuracy on GPU execution of manifold corrections method has a good agreement with the execution of codes on merely central processing unit (CPU-based) method. The acceleration ability when the codes are implemented on GPU can increase enormously through the use of shared memory and register optimization techniques without additional hardware costs, implying that the speedup is nearly 13 times as compared with the codes executed on CPU for phase space scan (including 314 314  orbits). In addition, GPU-accelerated manifold correction method is used to numerically study how dynamics are affected by the spin-induced quadrupole-monopole interaction for black hole binary system.

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Applying explicit symplectic-like methods to nonconservative nonseparable systems

Cited by 9 publications

References 19 publications

Chaotic motion of neutral and charged particles in a magnetized Ernst-Schwarzschild spacetime

Chaotic motion of neutral and charged particles in a magnetized Ernst-Schwarzschild spacetime

Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations

GPU accelerated manifold correction method for spinning compact binaries

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