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arXiv · 2404.12480

Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems

Jan Giesselmann·Attila Karsai·Tabea Tscherpel
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Abstract

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.

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Jan Giesselmann, Attila Karsai, Tabea Tscherpel. 2024-07-22. Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems. https://arxiv.org/abs/2404.12480

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