后牛顿哈密顿系统的高阶显式辛分裂方法
Efficient high-order explicit symplectic splitting methods for post-Newtonian Hamiltonian systems
AI总结：
提出一种新的扩展和分裂方法，用于后牛顿哈密顿系统，构建无阶降的高阶显式辛积分器，数值实验表明其长期守恒性和计算效率优于隐式方法和现有显式分裂技术。
摘要：
后牛顿哈密顿系统的不可分性通常需要使用计算昂贵的隐式积分器。最近的研究通过将动力学嵌入到双倍相空间中克服了这一限制，从而能够开发显式辛方法。然而，现有的专门设计的显式积分器在时间步长较小时（即 $h <\varepsilon^3$）会出现高阶方法的阶降。在本文中，我们提出了一种新的扩展和分裂方法，用于双倍哈密顿量，在此框架下可以构建专门设计的显式辛积分器。结果表明，所提出的积分器实现了真正的高阶收敛，没有阶降，并利用了小的后牛顿参数 $\varepsilon$。来自2PN自旋双星模拟的数值结果证明，与隐式方法和现有显式分裂技术相比，该方法具有优越的长期不变量守恒性和显著更高的计算效率。
英文摘要：
The nonseparability of post-Newtonian (PN) Hamiltonian systems typically necessitates the use of computationally expensive implicit integrators. Recent research overcomes this limitation by embedding the dynamics into a doubled phase space, which enables the development of explicit symplectic methods. However, existing specially designed explicit integrators suffer from order reduction for high-order methods when the time stepsize is small, i.e., $h <\varepsilon^3$. In this paper, we propose a novel extension and splitting approach for the doubled Hamiltonian, under which specially designed explicit symplectic integrators can be constructed. It is shown that the proposed integrators achieve genuine high-order convergence without order reduction and take advantage of the small PN parameter $\varepsilon$. Numerical results from simulations with 2PN spinning binaries demonstrate superior long-term conservation of invariants and significantly higher computational efficiency compared to both implicit methods and existing explicit splitting techniques.
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