Research output per year
Research output per year
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review
In this work, we present a piece-wise symplectic model order reduction (MOR) method for Hamiltonian systems on quadratically embedded manifolds. For Hamiltonian systems, which suffer from slowly decaying Kolmogorov N-widths, linear-subspace reduced-order models (ROMs) of low dimension can have insufficient accuracy. The recently proposed symplectic manifold Galerkin projection combined with the quadratic manifold cotangent lift approximation (QMCL) is a symplectic MOR method that can achieve higher accuracy than linear-subspace symplectic MOR methods. In this paper, we improve the online computational complexity and energy-preserving ability of the QMCL by proposing a piece-wise symplectic MOR approach. First, the QMCL map is approximated by a linear symplectic map on each discrete time-interval. Then, the symplectic Galerkin projection is applied to obtain a sequence of reduced-order Hamiltonian systems. In case that the Hamiltonian of the full-order model is a polynomial, the sequence of the Hamiltonians of the ROMs can be preserved up to a multiple of a pre-given tolerance used in the Newton iteration. In the numerical example, we investigate the approximation quality and the energy-preservation of the proposed algorithm.
Original language | English |
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Title of host publication | Numerical Mathematics and Advanced Applications ENUMATH 2023 |
Editors | Adélia Sequeira, Ana Silvestre, Svilen S. Valtchev, João Janela |
Publisher | Springer |
Pages | 355-364 |
Number of pages | 10 |
Volume | 1 - European Conference |
ISBN (Electronic) | 978-3-031-86173-4 |
ISBN (Print) | 978-3-031-86172-7, 978-3-031-86175-8 |
DOIs | |
Publication status | Published - 2025 |
Event | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2023 - Lisbon, Portugal Duration: 4 Sept 2023 → 8 Sept 2023 |
Name | Lecture Notes in Computational Science and Engineering |
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Publisher | Springer |
Volume | 153 |
ISSN (Print) | 1439-7358 |
ISSN (Electronic) | 2197-7100 |
Conference | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2023 |
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Abbreviated title | ENUMATH 2023 |
Country/Territory | Portugal |
City | Lisbon |
Period | 4/09/23 → 8/09/23 |
Research output: Working paper › Preprint › Academic