Performance of different correction maps in the extended phase-space method for spinning compact binaries

Luo, Junjie; Feng, J. H.; Zhang, Honghao; Lin, Weipeng

doi:10.1093/mnras/stac3494

Cited by 4 publications

(10 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These applications were successful in several examples, but not in chaotic orbits. However, our previous work [Luo et al(2021), Luo et al(2022)] proposed the manifold corrections map, which effectively overcame the challenge. Unlike that in the original paper [Luo et al(2021), Luo et al(2022)], the correction map for the 1PN Hamiltonian is…”

Section: Phase-space Expansion Methods With a Multi-factors Correctio...mentioning

confidence: 99%

“…Midpoint and correction maps [Luo et al(2017), Luo et al(2021)] have been proposed to ensure the equivalence of the original variables and the copy one. Recently, we proposed a multi-factor correction map that yields a higher accuracy of the phase-space expansion method without significant computational resource increases [Luo et al(2022)]. This paper aims to design a multi-factor correction map for post-Newton Hamiltonian and examine its performance.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian

et al. 2023

Self Cite

View full text Add to dashboard Cite

The equations of motion for a Lagrangian mainly refer to the acceleration equations, which can be obtained by the Euler–Lagrange equations. In the post-Newtonian Lagrangian form of general relativity, the Lagrangian systems can only maintain a certain post-Newtonian order and are incoherent Lagrangians since the higher-order terms are omitted. This truncation can cause some changes in the constant of motion. However, in celestial mechanics, Hamiltonians are more commonly used than Lagrangians. The conversion from Lagrangianto Hamiltonian can be achieved through the Legendre transformation. The coordinate momentum separable Hamiltonian can be computed by the symplectic algorithm, whereas the inseparable Hamiltonian can be used to compute the evolution of motion by the phase-space expansion method. Our recent work involves the design of a multi-factor correction map for the phase-space expansion method, known as the correction map method. In this paper, we compare the performance of the implicit algorithm in post-Newtonian Lagrangians and the correction map method in post-Newtonian Hamiltonians. Specifically, we investigate the extent to which both methods can uphold invariance of the motion’s constants, such as energy conservation and angular momentum preservation. Ultimately, the results of numerical simulations demonstrate the superior performance of the correction map method, particularly with respect to angular momentum conservation.

show abstract

Section: Phase-space Expansion Methods With a Multi-factors Correctio...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian

et al. 2023

Self Cite

View full text Add to dashboard Cite

show abstract

“…Now we list all the numerical methods used in the numerical experiments for comparison. 2ndKSYM-mp: the second order K-symplectic-like method with the midpoint permutation which is the method S 2 ˜defined in equation (32) or (37). 2ndKSYM-perm: the second order K-symplectic-like method with another permutation which is the method S 2 ˆdefined in equation (39) or (41).…”

Section: Methodsmentioning

confidence: 99%

“…These could be the reasons for the method's good performance in astrophysical applications [30]. Recently, the permutations of the extended phase space explicit symplectic-like methods have been further explored [31,32]. Numerical experiments demonstrate that for the cases of circular restricted three-body system or chaotic orbits of spinning compact binary, the midpoint permutation causes the secular energy drift [31].…”

Section: Introductionmentioning

confidence: 99%

“…Numerical experiments demonstrate that for the cases of circular restricted three-body system or chaotic orbits of spinning compact binary, the midpoint permutation causes the secular energy drift [31]. To overcome this problem, several kinds of permutations have been developed for the PN Hamiltonian of spinning compact binaries and the new permutations are more effective in simulating the chaotic orbits of spinning compact binaries [31,32]. Instead of imposing the permutation, Tao constructed a new augmented Hamiltonian in an extended phase space, consisting of two Pihajoki sub-Hamiltonians H A and H B and a third sub-Hamiltonian H C with the control parameter ω [33].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Explicit K-symplectic-like algorithms for guiding center system

Zhu,

Liu,

Zhu

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

In this paper, for the guiding center system, we propose a type of explicit K symplectic-like methods by extending the original guiding center phase space and constructing new augmented Hamiltonians. The original guiding center phase space is extended by making several copies in order to make the guiding center Hamiltonian separable. In the extended phase space, the augmented guiding center Hamiltonian can be numerically solved as a standard K-symplectic system through the splitting technique and the composition of some simpler subsystems. Meanwhile, a midpoint permutation constraint is imposed on the extended phase space. Numerical experiments are carried out for guiding center motions in different magnetic fields using different numerical methods, including K-symplectic-like algorithms, canonical symplectic algorithms, and higher order implicit Runge-Kutta methods. Results show that energy errors of K-symplectic-like methods are bounded within small intervals over long time, defeating higher order implicit Runge-Kutta methods. For comparison, explicit K-symplectic-like methods exhibit higher computational efficiency than existing canonicalized symplectic methods of the same order. We also verify that permutation constraints are important for the numerical properties of explicit K-symplectic methods.Among them,the method with the midpoint permutation constraint behaves better in long-term energy conservation and the elimination of secular drift errors than the same method without any permutation. The permutation that imposes a constraint on the Hamiltonian behaves best in energy preservation.

show abstract

Semiexplicit K‐symplectic‐like methods with energy conservation for noncanonical Hamiltonian systems

Zhu,

2024

Numerical Methods Partial

View full text Add to dashboard Cite

For the nonseparable noncanonical Hamiltonian systems, we propose efficient K‐symplectic‐like methods which are semiexplicit and energy‐preserving. By introducing two copies of the phase space and constructing an augmented Hamiltonian, we can separate the noncanonical Hamiltonian system into two explicitly integrable parts. Subsequently, explicit K‐symplectic methods can be constructed by using the splitting and composing method. To enforce constraints on the two copies of the phase space, we provide two transformations with energy conservation property. This enables us to obtain semiexplicit K‐symplectic‐like methods that preserve energy. Two algorithms are provided to implement the semiexplicit K‐symplectic‐like methods with energy conservation and their convergence has been proved. Numerical results on two noncanonical Hamiltonian systems demonstrate that the energy errors of our proposed methods remain bounded within machine precision over long time without exhibiting energy drift. Furthermore, the proposed methods exhibit superior computational efficiency compared to the canonicalized symplectic methods of the same order.

show abstract

Performance of different correction maps in the extended phase-space method for spinning compact binaries

Cited by 4 publications

References 26 publications

Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian

Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian

Explicit K-symplectic-like algorithms for guiding center system

Semiexplicit K‐symplectic‐like methods with energy conservation for noncanonical Hamiltonian systems

Contact Info

Product

Resources

About