论文标题
针对哈密顿动力学的明确的伪能量保存时间整合计划
An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics
论文作者
论文摘要
我们为汉密尔顿系统的时间整合提供了一种新的显式伪能和动量保护计划。该方案是正式的二阶精度，基于两个关键思想：自由飞行粒子之间力的时间段的集成和在离散时间节点时动量跳跃的使用，从而导致加速度的两步公式。伪能源保护是在精确的力整合下建立的，而在存在正交误差的情况下，二阶精度是有效的。此外，我们设计了该方案的异步版本，该版本可用于缓慢快速的时间步变策略的框架。该方案针对经典基准和非线性或不均匀波传播问题进行了验证。
We propose a new explicit pseudo-energy and momentum conserving scheme for the time integration of Hamiltonian systems. The scheme, which is formally second-order accurate, is based on two key ideas: the integration during the time-steps of forces between free-flight particles and the use of momentum jumps at the discrete time nodes leading to a two-step formulation for the acceleration. The pseudo-energy conservation is established under exact force integration, whereas it is valid to second-order accuracy in the presence of quadrature errors. Moreover, we devise an asynchronous version of the scheme that can be used in the framework of slow-fast time-stepping strategies. The scheme is validated against classical benchmarks and on nonlinear or inhomogeneous wave propagation problems.
