克服半周期时间步长障碍的动态多时间步长方法
Dynamical Multiple-Timestepping Methods for Overcoming the Half-Period Time Step Barrier
摘要：
目前的分子动力学模拟的生物分子使用多个时间步长来更新缓慢变化的力受到阻碍的不稳定性发生在时间步长等于最快的振动模式的周期的一半。这已经成为阻碍生物分子动力学长时间模拟的关键障碍。试图通过改变缓慢变化的力来驯服这种不稳定性，并努力通过朗之万动力学来抑制这种不稳定性，这并没有解决这种不稳定性的根本原因。在这项工作中，我们跟踪的不稳定性的非分析字符的基本频谱，并表明，正确的分裂的哈密顿量，使频谱分析，恢复稳定。由此产生的哈密顿量表明，除了由于缓慢变化的力而更新动量之外，还必须用修改的质量来更新位置。因此，多时间步长必须动态地完成。
英文摘要：
Current molecular dynamic simulations of biomolecules using multiple time steps to update the slowingly changing force are hampered by an instability occuring at time step equal to half the period of the fastest vibrating mode. This has became a critical barrier preventing the long time simulation of biomolecular dynamics. Attemps to tame this instability by altering the slowly changing force and efforts to damp out this instability by Langevin dynamics do not address the fundamental cause of this instability. In this work, we trace the instability to the non-analytic character of the underlying spectrum and show that a correct splitting of the Hamiltonian, which render the spectrum analytic, restores stability. The resulting Hamiltonian dictates that in additional to updating the momentum due to the slowly changing force, one must also update the position with a modified mass. Thus multiple-timestepping must be done dynamically.
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