Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911964118122496 |
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| author | Giesselmann, Jan Karsai, Attila Tscherpel, Tabea |
| author_facet | Giesselmann, Jan Karsai, Attila Tscherpel, Tabea |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12480 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems Giesselmann, Jan Karsai, Attila Tscherpel, Tabea Numerical Analysis 35K55, 37L65, 37K58, 65J08, 65J15, 65L60, 65M60, 65P10 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. |
| title | Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems |
| topic | Numerical Analysis 35K55, 37L65, 37K58, 65J08, 65J15, 65L60, 65M60, 65P10 |
| url | https://arxiv.org/abs/2404.12480 |