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math.NA2026
A discrete gradient scheme for preserving QSR-dissipativity
Attila Karsai, Philipp Schulze
The notion of dissipative dynamical systems provides a formal description of processes that cannot generate energy internally. For these systems, changes in energy can only occur d…
math.NA2025
Structure-Preserving Discretization and Model Reduction for Energy-Based Models
Robert Altmann, Attila Karsai, Philipp Schulze
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradien…
math.NA2024
Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems
Jan Giesselmann, Attila Karsai, Tabea Tscherpel
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-…