Speaker
Description
The convergence speed of linear model order reduction techniques cannot be better than the Kolmogorov N-width. The problem is that it is well-known that the Kolmogorov N-width of wave-type problems only decays slowly.
In this talk we will address the question to what extent discontinuous Galerkin Trefftz formulations of parametrized partial differential equations and its associated Trefftz spaces are suitable for model order reduction techniques. We construct non-linear model order reduction approaches using a specific discontinuous Galerkin Trefftz formulation of the wave equation.
Trefftz finite element formulations use trial and test functions that solve the corresponding PDE locally on each mesh element. In order to approximate the boundary conditions well, they cannot be continuous on the whole domain and therefore are discontinuous Galerkin methods by nature.
We are building on a specific formulation of the homogeneous wave equation, published by Andrea Moiola and Ilaria Perugia in 2018. It is a space-time approach considering the wave equation as a first-order system.
Subject to investigation is whether in non-linear model order reduction approaches the Trefftz spaces will provide reduced spaces that outperform the Kolmogorov N-width. The approaches are tested in numerical experiments. Although the work is still in its early stages, the results of the numerical experiments indicate that dG Trefftz methods have the potential to be well suited for efficient non-linear model order reduction techniques.
