Energy-Consistent Splitting and Decomposition Approaches for Coupled port-Hamiltonian ODEs
Abstract
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.
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BibTeX
@misc{monch2026energyconsistent,
title = {{Energy-Consistent Splitting and Decomposition Approaches for Coupled port-Hamiltonian ODEs}},
author = {Marius Mönch and Nicole Marheineke and Andreas Bartel and Kevin Schäfers and Michael Günther},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04884},
eprint = {2609.04884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04884},
}
RIS
TY - UNPB
TI - Energy-Consistent Splitting and Decomposition Approaches for Coupled port-Hamiltonian ODEs
AU - Marius Mönch
AU - Nicole Marheineke
AU - Andreas Bartel
AU - Kevin Schäfers
AU - Michael Günther
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04884
UR - https://arxiv.org/abs/2609.04884
AB - 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.
ER -