Structure preserving discretization method for 1D and 2D port-Hamiltonian systems using finite differences on staggered grids
Numerical Analysis
2025-12-09 v1 Numerical Analysis
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.
Cite
@article{arxiv.2512.07406,
title = {Structure preserving discretization method for 1D and 2D port-Hamiltonian systems using finite differences on staggered grids},
author = {Ignacio Diaz Alastuey and Yann Le Gorrec and Yongxin Wu},
journal= {arXiv preprint arXiv:2512.07406},
year = {2025}
}