Semiexplicit Symplectic Integrators for Non-separable Hamiltonian Systems
Semiexplicit Symplectic Integrators for Non-separable Hamiltonian Systems
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DOI：
10.1090/mcom/3778
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发表时间：
2021-11
期刊：
影响因子：
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通讯作者：
B.P.A. Jayawardana;T. Ohsawa
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文献类型：
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作者：
B.P.A. Jayawardana;T. Ohsawa
结合Pihajoki的扩展相空间方法和对称投影方法，我们构造了不可分Hamilton系统的辛积分器。由此产生的方法是半显式的意义上说，主要的时间演化步骤是明确的，而对称投影步骤是隐式的。对称投影绑定潜在的分歧副本的解决方案，从而弥补了扩展相空间方法的主要缺点。此外，我们的半显式方法是辛的原始相空间。这与现有的扩展相空间积分器相反，扩展相空间积分器仅在扩展相空间中是辛的。我们证明，我们的方法具有很好的长期保存的不变量，它往往是一样快，可以比陶显式修改的扩展相空间积分特别是足够小的时间步长和高阶实现和高维问题更快。
We construct a symplectic integrator for non-separable Hamiltonian systems combining an extended phase space approach of Pihajoki and the symmetric projection method. The resulting method is semiexplicit in the sense that the main time evolution step is explicit whereas the symmetric projection step is implicit. The symmetric projection binds potentially diverging copies of solutions, thereby remedying the main drawback of the extended phase space approach. Moreover, our semiexplicit method is symplectic in the original phase space. This is in contrast to existing extended phase space integrators, which are symplectic only in the extended phase space. We demonstrate that our method exhibits an excellent long-time preservation of invariants, and also that it tends to be as fast as and can be faster than Tao's explicit modified extended phase space integrator particularly for small enough time steps and with higher-order implementations and for higher-dimensional problems.