Improved a posteriori error bounds for reduced port-Hamiltonian systems

Authors

Johannes Rettberg, Dominik Wittwar, Patrick Buchfink, Robin Herkert, Jörg Fehr, Bernard Haasdonk

Abstract

Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically known to be highly pessimistic in the sense of largely overestimating the true error. This work applies two improved error bounding techniques, namely (a)  a hierarchical error bound and (b)  an error bound based on an auxiliary linear problem , to the case of port-Hamiltonian systems. The approaches rely on a secondary approximation of (a) the dynamical system and (b) the error system. In this paper, these methods are adapted to port-Hamiltonian systems. The mathematical relationship between the two methods is discussed both theoretically and numerically. The effectiveness of the described methods is demonstrated using a challenging three-dimensional port-Hamiltonian model of a classical guitar with fluid–structure interaction.

Keywords

Structure-preserving model order reduction; A posteriori error control; Port-Hamiltonian system; Fluid–structure interaction; 65L70; 34C20

Citation

• Journal: Advances in Computational Mathematics
• Year: 2024
• Volume: 50
• Issue: 5
• Pages:
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s10444-024-10195-8

BibTeX

@article{Rettberg_2024,
  title={{Improved a posteriori error bounds for reduced port-Hamiltonian systems}},
  volume={50},
  ISSN={1572-9044},
  DOI={10.1007/s10444-024-10195-8},
  number={5},
  journal={Advances in Computational Mathematics},
  publisher={Springer Science and Business Media LLC},
  author={Rettberg, Johannes and Wittwar, Dominik and Buchfink, Patrick and Herkert, Robin and Fehr, Jörg and Haasdonk, Bernard},
  year={2024}
}

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