Improved a posteriori error bounds for reduced port-Hamiltonian systems Article Swipe

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

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.1007/s10444-024-10195-8

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.

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Computational Science and Engineering A priori and a posteriori Mathematics Hamiltonian system Port (circuit theory) Hamiltonian (control theory) Algebra over a field Applied mathematics Calculus (dental) Mathematical optimization Pure mathematics Mathematical analysis Medicine Epistemology Engineering Dentistry Electrical engineering Philosophy

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Type: article
Language: en
Landing Page: https://doi.org/10.1007/s10444-024-10195-8
OA Status: hybrid
Cited By: 3
References: 60
Related Works: 10
OpenAlex ID: https://openalex.org/W4402450308

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DOI: https://doi.org/10.1007/s10444-024-10195-8

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Title: Improved a posteriori error bounds for reduced port-Hamiltonian systems

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Language: en

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Publication year: 2024

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Publication date: 2024-09-11

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

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Landing page: https://doi.org/10.1007/s10444-024-10195-8

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Concepts: Computational Science and Engineering, A priori and a posteriori, Mathematics, Hamiltonian system, Port (circuit theory), Hamiltonian (control theory), Algebra over a field, Applied mathematics, Calculus (dental), Mathematical optimization, Pure mathematics, Mathematical analysis, Medicine, Epistemology, Engineering, Dentistry, Electrical engineering, Philosophy

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Cited by: 3

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