Implicit port-Hamiltonian systems: structure-preserving discretization for the nonlocal vibrations in a viscoelastic nanorod, and for a seepage model

Authors

Antoine Bendimerad-Hohl, Ghislain Haine, Laurent Lefèvre, Denis Matignon

Abstract

A structure-preserving partitioned finite element method (PFEM), for the semi-discretization of infinite-dimensional explicit port-Hamiltonian systems (pHs), is extended to those pHs of implicit type, leading to port-Hamiltonian differential Algebraic Equations (pH-DAE). Two examples are dealt with: the nonlocal vibrations in a viscoelastic nanorod in 1D, and the dynamics of a fluid filtration model, the Dzektser seepage model in 2D, for which illustrative numerical simulations are provided.

Keywords

port-Hamiltonian systems; Structure-Preserving Discretization; Partitioned Finite Element Method; Implicit port-Hamiltonian systems; Nonlocal dynamics

Citation

• Journal: IFAC-PapersOnLine
• Year: 2023
• Volume: 56
• Issue: 2
• Pages: 6789–6795
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2023.10.387
• Note: 22nd IFAC World Congress- Yokohama, Japan, July 9-14, 2023

BibTeX

@article{Bendimerad_Hohl_2023,
  title={{Implicit port-Hamiltonian systems: structure-preserving discretization for the nonlocal vibrations in a viscoelastic nanorod, and for a seepage model}},
  volume={56},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2023.10.387},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Bendimerad-Hohl, Antoine and Haine, Ghislain and Lefèvre, Laurent and Matignon, Denis},
  year={2023},
  pages={6789--6795}
}

Download the bib file

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