Structure-preserving model reduction for port-Hamiltonian systems based on separable nonlinear approximation ansatzes

Authors

Philipp Schulze

Abstract

We discuss structure-preserving model order reduction for port-Hamiltonian systems based on a nonlinear approximation ansatz which is linear with respect to a part of the state variables of the reduced-order model. In recent years, such nonlinear approximation ansatzes have gained more and more attention especially due to their effectiveness in the context of model reduction for transport-dominated systems which are challenging for classical linear model reduction techniques. We demonstrate that port-Hamiltonian reduced-order models can often be obtained by a residual minimization approach where a suitable weighted norm is used for the residual. Moreover, we discuss sufficient conditions for the resulting reduced-order models to be stable. Finally, the methodology is illustrated by means of two transport-dominated numerical test cases, where the ansatz functions are determined based on snapshot data of the full-order state.

Citation

• Journal: Frontiers in Applied Mathematics and Statistics
• Year: 2023
• Volume: 9
• Issue:
• Pages:
• Publisher: Frontiers Media SA
• DOI: 10.3389/fams.2023.1160250

BibTeX

@article{Schulze_2023,
  title={{Structure-preserving model reduction for port-Hamiltonian systems based on separable nonlinear approximation ansatzes}},
  volume={9},
  ISSN={2297-4687},
  DOI={10.3389/fams.2023.1160250},
  journal={Frontiers in Applied Mathematics and Statistics},
  publisher={Frontiers Media SA},
  author={Schulze, Philipp},
  year={2023}
}

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