Geometric optimization for structure-preserving model reduction of Hamiltonian systems

Thomas Bendokat*, Ralf Zimmermann*

*Kontaktforfatter

Publikation: Kapitel i bog/rapport/konference-proceedingKonferencebidrag i proceedingsForskningpeer review

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Abstract

Classical model reduction methods disregard the special symplectic structure associated with Hamiltonian systems. A key challenge in projection-based approaches is to construct a symplectic basis that captures the essential system information. This necessitates the computation of a so-called proper symplectic decomposition (PSD) of a given sample data set. The PSD problem allows for a canonical formulation as an optimization problem on the symplectic
Stiefel manifold. However, as with their Euclidean counterparts, symplectic projectors only depend on the underlying symplectic subspaces and not on the selected symplectic bases. This motivates to tackle the PSD problem as a Riemannian optimization problem on the symplectic Grassmann manifold, i.e., the matrix manifold of symplectic projectors. Initial investigations on this manifold feature in a recent preprint of the authors. In this work, we investigate
the feasibility and performance of this approach on two academic numerical examples. More precisely, we calculate an optimized PSD for snapshot matrices that stem from solving the one-dimensional linear wave equation and the one-dimensional nonlinear Schrödinger equation.
OriginalsprogEngelsk
Titel10th Vienna International Conference on Mathematical Modelling : MATHMOD 2022
Vol/bind55
ForlagElsevier
Publikationsdato2022
Udgave20
Sider457-462
DOI
StatusUdgivet - 2022
Begivenhed10th Vienna International Conference on Mathematical Modelling: MATHMOD 2022 - Wien, Østrig
Varighed: 27. jul. 202229. jul. 2022
Konferencens nummer: 10

Konference

Konference10th Vienna International Conference on Mathematical Modelling
Nummer10
Land/OmrådeØstrig
ByWien
Periode27/07/202229/07/2022
NavnIFAC-PapersOnLine
ISSN2405-8963

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