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arXiv · 2512.07406

Structure preserving discretization method for 1D and 2D port-Hamiltonian systems using finite differences on staggered grids

Ignacio Diaz Alastuey·Yann Le Gorrec·Yongxin Wu
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Abstract

This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the wave equation to a broader class of systems characterized by interconnection operators that include both differential and non-differential terms, such as the Timoshenko beam equation. The paper then introduces a discretization strategy for the two-dimensional case that requires only two grids, thereby accommodating a wider range of systems, including those whose interconnection operators contain non-differential components, such as the Mindlin plate model.

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Ignacio Diaz Alastuey, Yann Le Gorrec, Yongxin Wu. 2025-12-08. Structure preserving discretization method for 1D and 2D port-Hamiltonian systems using finite differences on staggered grids. https://arxiv.org/abs/2512.07406

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