Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems
<|reference_start|>Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems: For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The finite or infinite-dimensional system under consideration possesses a Hamiltonian function, which represents an energy in the system and is conserved or dissipated along solutions. For infinite-dimensional systems this structure is preserved under suitable Galerkin discretization in space. The numerical scheme is energy-consistent in the sense that the Hamiltonian of the approximate solutions at time grid points behaves accordingly. This structure preservation property is achieved by specific design of a continuous Petrov-Galerkin (cPG) method in time. It coincides with standard cPG methods in special cases, in which the latter are energy-consistent. Examples of port-Hamiltonian ODEs and PDEs are presented to visualize the framework. In numerical experiments the energy consistency is verified and the convergence behavior is investigated.<|reference_end|>
@article{giesselmann2024energy-consistent,
    title={Energy-consistent Petrov-Galerkin time discretization of
  port-Hamiltonian systems},
    author={Jan Giesselmann, Attila Karsai, Tabea Tscherpel},
    journal={arXiv preprint arXiv:2404.12480},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.12480},
    primaryClass={math.NA cs.NA}
}