耦合端口哈密顿常微分方程的能量一致分裂与分解方法
Energy-Consistent Splitting and Decomposition Approaches for Coupled port-Hamiltonian ODEs
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中文总结 AI 辅助
本研究以耦合端口哈密顿常微分方程为对象，提出能量一致性准则，推导分裂继承系统能量行为的充分条件，经数值实验证实保留子流端口哈密顿结构对能量一致分裂至关重要，时间尺度分解可提升多速率系统计算效率。
中文摘要 AI 辅助
算子分裂为（耦合）端口哈密顿系统的数值积分提供了一种极具吸引力的方法，因为它允许在各个子问题层面利用底层系统结构。然而，分解的选择并非唯一，可能会强烈影响计算效率和原始系统能量行为的保持。在本研究中，我们系统地探讨了这种相互作用，并引入能量一致性作为评估端口哈密顿常微分方程分裂方法的准则。我们推导了基于给定分解的分裂继承连续系统能量行为的充分条件，并利用这些条件分析了耦合端口哈密顿系统的几种分解策略。特别地，我们对比了保留结构的分解与利用低维子系统动力学或分离时间尺度的方法。分析通过使用Strang分裂及其多时间步扩展的数值实验得到补充。采用具有快速电气和缓慢热动力学的可扩展电热基准来评估精度、能量行为和计算效率。结果表明，保持子流的端口哈密顿结构对能量一致分裂至关重要，而利用子系统结构或时间尺度分离的分解可提供显著的计算优势。特别是，时间尺度分解在具有明显多速率特性的系统中产生了显著的效率提升，而破坏结构的分解可能导致不期望的能量行为。
英文摘要
Operator splitting provides an attractive approach for the numerical integration of (coupled) port-Hamiltonian systems, as it allows the underlying system structure to be exploited at the level of the individual subproblems. However, the choice of the decomposition is not unique and may strongly affect both the computational efficiency and the preservation of the energy behavior of the original system. In this work, we investigate this interplay systematically and introduce energy consistency as a criterion for assessing splitting methods for port-Hamiltonian ordinary differential equations. We derive sufficient conditions under which a splitting based on a given decomposition inherits the energy behavior of the continuous system and use these conditions to analyze several decomposition strategies for coupled port-Hamiltonian systems. In particular, we compare decompositions that preserve the structure with approaches that exploit lower-dimensional subsystem dynamics or separated time scales. The analysis is complemented by numerical experiments using Strang splitting and its multiple-time-stepping extension. A scalable electro-thermal benchmark with fast electrical and slow thermal dynamics is employed to assess accuracy, energy behavior, and computational efficiency. The results demonstrate that preserving the port-Hamiltonian structure of the subflows is essential for energy-consistent splitting, whereas decompositions that exploit subsystem structure or time-scale separation can provide substantial computational advantages. In particular, the time-scale decomposition yields significant efficiency gains for systems with pronounced multirate characteristics, while structure-destroying decompositions may lead to undesirable energy behavior.
发表机构
- Trier University（特里尔大学）
- University of Wuppertal（伍珀塔尔大学）
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