Weak Form of the Stokes-Dirac Structure and Geometric Discretization of Port-Hamiltonian Systems

Abstract : We present the mixed Galerkin discretization of distributed-parameter port-Hamiltonian systems. Due to the inherent definition of (boundary) interconnection ports, this system representation is particularly useful for the modeling of interconnected multi-physics systems and control. At the prototypical example of a system of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure, (ii) its geometric approximation by a finite-dimensional Dirac structure using a mixed Galerkin approach and power-preserving maps on the space of discrete power variables and (iii) the approximation of the Hamiltonian to obtain finite-dimensional port-Hamiltonian state space models. The power-preserving maps on the discrete bond space offer design degrees of freedom for the discretization, which is illustrated at the example Whitney finite elements on a 2D simplicial triangulation. The resulting schemes can be considered as trade-offs between centered approximations and upwinding.
Type de document :
Article dans une revue
Journal of Computational Physics, Elsevier, 2018, 361, pp.442-476. 〈10.1016/j.jcp.2018.02.006〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01831948
Contributeur : Laurent Lefèvre <>
Soumis le : vendredi 6 juillet 2018 - 13:29:30
Dernière modification le : mercredi 20 mars 2019 - 15:30:35
Document(s) archivé(s) le : mardi 2 octobre 2018 - 04:07:59

Fichier

Weak-form-discretization-PHS-2...
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

P Kotyczka, B. Maschke, Laurent Lefèvre. Weak Form of the Stokes-Dirac Structure and Geometric Discretization of Port-Hamiltonian Systems. Journal of Computational Physics, Elsevier, 2018, 361, pp.442-476. 〈10.1016/j.jcp.2018.02.006〉. 〈hal-01831948〉

Partager

Métriques

Consultations de la notice

35

Téléchargements de fichiers

62