Structure-Preserving Time Discretization of Port-Hamiltonian Systems via Discrete Gradient Pairs

Authors

Abstract

We discuss structure-preserving time discretization for nonlinear port-Hamiltonian systems with state-dependent mass matrix. Such systems occur, for instance, in the context of structure-preserving nonlinear model order reduction for port-Hamiltonian systems and, in this context, structure-preserving time discretization is crucial for preserving some of the properties of the time-continuous reduced-order model. For this purpose, we introduce a new class of time discretization schemes which is based on so-called discrete gradient pairs and leads to an exact power balance on the time-discrete level. Moreover, for the special case of a pointwise symmetric and positive definite mass matrix, we present an explicit construction of a discrete gradient pair. Finally, we illustrate the theoretical findings by means of a numerical example, where the time-continuous system is a nonlinear reduced-order model for an advection–diffusion problem.

Keywords

discrete gradient methods, port-hamiltonian systems, structure-preserving time discretization

Citation

ISBN: 9783032204035
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-20404-2_47
Note: European Consortium for Mathematics in Industry

BibTeX

@inbook{Schulze_2026,
  title={{Structure-Preserving Time Discretization of Port-Hamiltonian Systems via Discrete Gradient Pairs}},
  ISBN={9783032204042},
  ISSN={2198-3283},
  DOI={10.1007/978-3-032-20404-2_47},
  booktitle={{Progress in Industrial Mathematics at ECMI 2023}},
  publisher={Springer Nature Switzerland},
  author={Schulze, Philipp},
  year={2026},
  pages={501--511}
}

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