OS Numerical Optimization: Compatible structure-preserving discretization and model reduction of a network problem

Dienstag, 23. April 2024
15:15 bis 16:45 Uhr


Veranstaltet von
B. Azmi & S. Volkwein

Vortragende Person/Vortragende Personen:
Dr. Björn L.-Sailer

On 23th April 2024 at 15:15, Dr. Björn L.-Sailer from the Austrian Academy of Sciences: Johann Radon InstituteI for Computatinonal and Cpplied Mathematics (RICAM) will give a talk.

Abstract: Structure-preserving approximation is still an active research area. By preserving or mimicking relevant geometric structures such as, e.g., conservation laws or symplecticities, unphysical solution behavior and numerical instabilities can be avoided in many cases. The model problem considered in this contribution describes nonlinear flows on networks. It covers a hierarchy of models used to describe gas network systems, including particularly the barotropic Euler equations.

Our discretization and model reduction approach is analyzed using energy-based modeling concepts, such as the port-Hamiltonian formalism and the so-called partial Legendre-transformation. The latter offers an elegant approach for the systematic analysis of certain variable transformations, which widens the range of formulations, for which structure-preserving Galerkin-type approximations can be derived under a few compatibility conditions, using variational arguments only.

A particular focus of the talk also lies on the realization of the snapshot-based model order- and complexity-reduction. While beneficial for the robustness and performance of the reduced models, the compatibility conditions pose a challenge in the training phase. Appropriate adaptions of the conventional model reduction methods will be presented.