Optimal Bases for Symplectic Model Order Reduction of Canonizable Linear Hamiltonian Systems

Patrick Buchfink*, Silke Glas, Bernard Haasdonk

*Corresponding author for this work

Research output: Contribution to journalConference articleAcademicpeer-review

3 Citations (Scopus)
49 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)463-468
Number of pages6
Issue number20
Publication statusPublished - 2022
Event10th Vienna International Conference on Mathematical Modelling, MATHMOD 2022 - Vienna, Austria
Duration: 27 Jul 202229 Jul 2022
Conference number: 10


  • Hamiltonian systems
  • Optimal basis generation
  • Proper orthogonal decomposition (POD)
  • Proper symplectic decomposition
  • Symplectic model reduction


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