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.
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Journal of Computational Physics, Elsevier, 2018
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https://hal.archives-ouvertes.fr/hal-01831948
Contributeur : Laurent Lefèvre <>
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Dernière modification le : jeudi 19 juillet 2018 - 01:06:56
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  • HAL Id : hal-01831948, version 1

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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. 〈hal-01831948〉

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