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

2025/12/08 by Ignacio Diaz Alastuey, Alastuey, Ignacio Diaz, Yann Le Gorrec +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Control and Stability of Dynamical Systems #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2512.07406

openalex publication_date 2025/12/08 · openalex created_date 2025/12/09 · openalex updated_date 2026/07/28

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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