Symplectic model order reduction is a structure-preserving reduction technique for Hamiltonian systems. Apart from theoretical results like the preservation of stability, it has been demonstrated to give improved numerical results compared to classical MOR techniques. A key element in this procedure is the choice of a good symplectic reduced order basis (ROB). In our work, we introduce so-called canonizable Hamiltonian systems in energy coordinates. For such systems with the assumption of a periodic solution, we derive a globally optimal symplectic ROB in the sense of the proper symplectic decomposition (PSD). To this end, we show that the proper orthogonal decomposition (POD) of a canonizable Hamiltonian system is automatically symplectic from which we deduce optimality of the PSD. To verify our findings numerically, we consider a reproduction experiment for the linear wave equation.
%0 Conference Paper
%1 Buchfink2022
%A Buchfink, Patrick
%A Glas, Silke
%A Haasdonk, Bernard
%B 10th Vienna International Conference on Mathematical Modelling MATHMOD 2022
%D 2022
%J IFAC-PapersOnLine
%K EXC2075 PN5 PN5-7 selected
%N 20
%P 463--468
%R 10.1016/j.ifacol.2022.09.138
%T Optimal Bases for Symplectic Model Order Reduction of Canonizable Linear Hamiltonian Systems
%V 55
%X Symplectic model order reduction is a structure-preserving reduction technique for Hamiltonian systems. Apart from theoretical results like the preservation of stability, it has been demonstrated to give improved numerical results compared to classical MOR techniques. A key element in this procedure is the choice of a good symplectic reduced order basis (ROB). In our work, we introduce so-called canonizable Hamiltonian systems in energy coordinates. For such systems with the assumption of a periodic solution, we derive a globally optimal symplectic ROB in the sense of the proper symplectic decomposition (PSD). To this end, we show that the proper orthogonal decomposition (POD) of a canonizable Hamiltonian system is automatically symplectic from which we deduce optimality of the PSD. To verify our findings numerically, we consider a reproduction experiment for the linear wave equation.
@inproceedings{Buchfink2022,
abstract = {Symplectic model order reduction is a structure-preserving reduction technique for Hamiltonian systems. Apart from theoretical results like the preservation of stability, it has been demonstrated to give improved numerical results compared to classical MOR techniques. A key element in this procedure is the choice of a good symplectic reduced order basis (ROB). In our work, we introduce so-called canonizable Hamiltonian systems in energy coordinates. For such systems with the assumption of a periodic solution, we derive a globally optimal symplectic ROB in the sense of the proper symplectic decomposition (PSD). To this end, we show that the proper orthogonal decomposition (POD) of a canonizable Hamiltonian system is automatically symplectic from which we deduce optimality of the PSD. To verify our findings numerically, we consider a reproduction experiment for the linear wave equation.},
added-at = {2025-02-14T11:14:18.000+0100},
author = {Buchfink, Patrick and Glas, Silke and Haasdonk, Bernard},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2f119ca019bfeeb14600c78ea425cab2b/simtechpuma},
booktitle = {10th Vienna International Conference on Mathematical Modelling MATHMOD 2022},
doi = {10.1016/j.ifacol.2022.09.138},
interhash = {450de239e2c70bc72fc2be9540cb2dd5},
intrahash = {f119ca019bfeeb14600c78ea425cab2b},
issn = {2405-8963},
journal = {IFAC-PapersOnLine},
keywords = {EXC2075 PN5 PN5-7 selected},
number = 20,
pages = {463--468},
timestamp = {2025-02-14T11:14:18.000+0100},
title = {Optimal Bases for Symplectic Model Order Reduction of Canonizable Linear Hamiltonian Systems},
volume = 55,
year = 2022
}
