Work

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

Year: 2025

Type: article

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.

Source: SMAI Journal of Computational Mathematics

DOI: 10.5802/smai-jcm.127

Authors: Jan Giesselmann, Attila Karsai, Tabea Tscherpel

Institutions: Technische Universität Darmstadt, Technische Universität Berlin

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Deutsche Forschungsgemeinschaft

Awards: TRR 154: Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken, G6692072944