Discrete gradient methods for port-Hamiltonian differential-algebraic equations

Authors

Philipp L. Kinon, Riccardo Morandin, Philipp Schulze

Abstract

Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient methods to the system class of nonlinear port-Hamiltonian differential-algebraic equations - as they emerge from the port- and energy-based modeling of physical systems in various domains. We introduce a novel numerical scheme tailored for semi-explicit differential-algebraic equations and further address more general settings using the concepts of discrete gradient pairs and Dirac-dissipative structures. Additionally, the behavior under system transformations is investigated and we demonstrate that under suitable assumptions port-Hamiltonian differential-algebraic equations admit a representation which consists of a parametrized port-Hamiltonian semi-explicit system and an unstructured equation. Finally, we present the application to multibody system dynamics and discuss numerical results to demonstrate the capabilities of our approach.

Keywords

differential-algebraic equations, discrete gradients, port-hamiltonian systems, structure-preserving discretization, time integration methods

Citation

• Journal: Applied Numerical Mathematics
• Year: 2025
• Volume:
• Issue:
• Pages:
• Publisher: Elsevier BV
• DOI: 10.1016/j.apnum.2025.12.006

BibTeX

@article{Kinon_2025,
  title={{Discrete gradient methods for port-Hamiltonian differential-algebraic equations}},
  ISSN={0168-9274},
  DOI={10.1016/j.apnum.2025.12.006},
  journal={Applied Numerical Mathematics},
  publisher={Elsevier BV},
  author={Kinon, Philipp L. and Morandin, Riccardo and Schulze, Philipp},
  year={2025}
}

Download the bib file

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