Discretization of Dirac systems and port-Hamiltonian systems: the role of the constraint algorithm

Authors

María Barbero-Liñán, Juan Manuel López Medel, David Martín de Diego

Abstract

We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian systems and we discuss how to merge the discretization procedure and the constraint algorithm associated to systems of implicit differential equations. After fixing a time step, discretization maps are used to discretize the configuration manifold and we obtain different geometric integrators for the given implicit differential equations. As a result we propose a new method that exactly preserves the integrable part of those equations.

Keywords

34a26, 34c40, 37j39, 53d17, 65p10

Citation

• Journal: Numerische Mathematik
• Year: 2026
• Volume:
• Issue:
• Pages:
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00211-026-01560-4

BibTeX

@article{Barbero_Li_n_2026,
  title={{Discretization of Dirac systems and port-Hamiltonian systems: the role of the constraint algorithm}},
  ISSN={0945-3245},
  DOI={10.1007/s00211-026-01560-4},
  journal={Numerische Mathematik},
  publisher={Springer Science and Business Media LLC},
  author={Barbero-Liñán, María and López Medel, Juan Manuel and Martín de Diego, David},
  year={2026}
}

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