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

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.

To cite this paper:
Bendimerad-Hohl Antoine, Haine Ghislain, Lefèvre Laurent, Matignon Denis (2023) Implicit port-Hamiltonian systems: structure-preserving discretization for the nonlocal vibrations in a viscoelastic nanorod, and for a seepage model. IFAC-PapersOnLine 56(2):6789–6795. Yokohama, Japan.

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