Explicit structure-preserving discretization of port-Hamiltonian systems with mixed boundary control

Authors

Andrea Brugnoli, Ghislain Haine, Denis Matignon

Abstract

In this contribution, port-Hamiltonian systems with non-homogeneous mixed boundary conditions are discretized in a structure-preserving fashion by means of the Partitioned FEM. This means that the power balance and the port-Hamiltonian structure of the continuous equations is preserved at the discrete level. The general construction relies on a weak imposition of the boundary conditions by means of the Hellinger-Reissner variational principle, as recently proposed in [Thoma et al., 2021]. The case of linear hyperbolic wave-like systems, including the elastodynamic problem and the Maxwell equations in 3D, is then illustrated in detail. A numerical example is worked out on the case of the wave equation.

Keywords

Port-Hamiltonian systems (pHs); Partitioned Finite Element Method (PFEM); Mixed Boundary Control

Citation

• Journal: IFAC-PapersOnLine
• Year: 2022
• Volume: 55
• Issue: 30
• Pages: 418–423
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2022.11.089
• Note: 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022- Bayreuth, Germany, September 12-16, 2022

BibTeX

@article{Brugnoli_2022,
  title={{Explicit structure-preserving discretization of port-Hamiltonian systems with mixed boundary control}},
  volume={55},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2022.11.089},
  number={30},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Brugnoli, Andrea and Haine, Ghislain and Matignon, Denis},
  year={2022},
  pages={418--423}
}

Download the bib file

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