Silke Glas (DAMUT-MAST)

Date: 02 March 2022

Time: 12:45 – 13:15. Hours

Room:  RA1501 & online

Speaker: Silke Glas (DAMUT-MAST)


Title: "Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds”


Classical model reduction techniques project the governing equations onto linear subspaces of the high-dimensional state-space. However, for problems with slowly decaying Kolmogorov-n-widths such as certain transport-dominated problems, classical linear-subspace reduced order models (ROMs) of low dimension might yield inaccurate results. Thus, the reduced space needs to be extended to more general nonlinear manifolds. Moreover, as we are dealing with Hamiltonian systems, it is crucial that the underlying symplectic structure is preserved in the reduced model.

To the best of our knowledge, existing literatures addresses either model reduction on manifolds or symplectic model reduction for Hamiltonian systems, but not their combination. In this talk, we bridge these two approaches by providing a novel projection technique called symplectic manifold Galerkin, which projects the Hamiltonian system onto a nonlinear symplectic trial manifold such that the ROM is again a Hamiltonian system. We provide numerical results which demonstrate the ability of the method to outperform linear-subspace ROMs.