The present work deals with the numerical long-time integration of damped Hamiltonian systems. The method that we analyze combines a specific Strang splitting, that separates linear dissipative effects from conservative ones, with an energy-preserving averaged vector field (AVF) integrator for the Hamiltonian subproblem. This construction faithfully reproduces the energy-dissipation structure of the continuous model, its equilibrium points and its natural Lyapunov function. As a consequence of these structural similarities, both the convergence to equilibrium and, more interestingly, the energy decay rate of the continuous dynamical system are recovered at a discrete level. The possibility of replacing the implicit AVF integrator by an explicit Störmer-Verlet one is also discussed, while numerical experiments illustrate and support the theoretical findings.

中文翻译：

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阻尼哈密顿系统的保结构积分器的渐近分析

目前的工作涉及阻尼哈密顿系统的数值长期积分。我们分析的方法将特定的Strang分裂与线性能量耗散效应与保守效应分开，并结合了哈密顿量子问题的节能平均矢量场（AVF）积分器。该构造忠实地再现了连续模型的能量耗散结构，其平衡点和其自然Lyapunov函数。由于这些结构上的相似性，收敛到平衡状态，以及更有趣的是，连续动态系统的能量衰减率都在离散的水平上恢复。还讨论了用显式Störmer-Verlet代替隐式AVF积分器的可能性，