Philipp Schulze (TU Berlin)
Abstract: Projection-based model order reduction (MOR) aims for reduced-order models (ROMs) with low approximation errors and computation times. Apart from these quantitative measures, the preservation of qualitative properties is another important aspect in this context. For instance, the preservation of stability is desirable to prevent unphysical results and exponentially growing approximation errors. However, a classical Galerkin or Petrov-Galerkin projection does in general not preserve such properties. For instance, when applying classical MOR techniques to transport-dominated systems, this often leads to unstable ROMs. One approach to overcome such issues is structure-preserving MOR, which aims for preserving qualitative properties by preserving an algebraic or geometric structure encoding the desired properties.
In this talk, we focus on structure-preserving MOR for port-Hamiltonian and other energy-based structures. They have in common that the structure guarantees an energy balance, which implies passivity and often also Lyapunov stability. We demonstrate that a modified Petrov-Galerkin projection approach can be used to preserve the structure and, therefore, the associated properties. Next to classical MOR based on linear subspace approximations, we also address methods which are based on nonlinear manifolds and more suitable for transport-dominated systems. We demonstrate the theoretical findings by means of numerical examples.
Parts of this talk are joint work with R. Altmann (OvGU Magdeburg) and A. Karsai (TU Berlin).
