Vorträge

Partial differential equations model a wide range of physical phenomena.
Unfortunately, most of them cannot be solved directly, making it necessary
to develop efficient and robust numerical solution methods. In this talk,
we focus on two different ones: Radial basis functions (RBFs) and finite volume
methods (FVM). The former allow to solve differential equations without the
cumbersome generation of a grid. Moreover, RBFs can be used to improve flawed grids.
The latter are particularly useful in the context of semiconductor device simulation.
They yield robust numerical solutions even in the presence of boundary layers. The presented
finite volume scheme additionally satisfies a discrete maximum principle, just like the
continuous semiconductor equations (the van Roosbroeck system).

Tsunami modeling is - to first (and very accurate) approximation - performed with the help of shallow water theory and equations. This is still the method of choice for many applications, including forecasting, hazard assessment and inundation modeling. However, for long propagation distances as well as highly nonuniform topographies dispersive effects become important. While truly dispersive model equations are fully three-dimensional and therefore expensive with respect to computational requirements, a common approach to dispersive modeling comprises a non-hydrostatic correction of shallow water equations. In order to derive this correction term, a linear system of equations needs to be solved in each time step - even when the time-stepping scheme is explicit.

In the presentation we will introduce the basic modeling concepts for tsunami simulation, will show the derivation of non-hydrostatic correction terms and motivate further research on solvers for linear systems of equations.

We give new conditions for strong convergence of positive operator
semigroups as time tends to infinity. This is achieved by a new approach
that combines the splitting theorem by Jacobs, de Leeuw and Glicksberg
with a purely algebraic result about positive group representations.
Thus, we obtain convergence theorems not only for one-parameter
semigroups but also for a much larger class of semigroup representations
without any continuity or regularity assumption in time.
In particular, this generalizes results from the literature that, under
technical assumptions, a bounded positive strongly continuous semigroup
that contains or dominates a kernel operator converges strongly as time
tends to infinity. One can also derive a generalization of a famous
theorem by Doob for operator semigroups on the space of measures.

Ich werde in einem ca. 45 minütigen Vortrag meine Masterarbeit, die ich im Juni 2016 an der Uni Lund verteidigt habe, vorstellen.
Die Arbeit mit dem Titel ''Evaluation of a Gradient Free and a Gradient Based Optimization Algorithm for Industrial Beverage Pasteurisation Described by Different Modeling Variants'' entstand in Zusammenarbeit mit der Firma Krones AG in Kopenhagen.
Ziel ist die Optimierung thermaler Behandlung von Getränken und flüssigen Dosenkonserven. Dazu wurden Pasteurisierungsprozesse mathematisch formuliert, simuliert und die Optimierung mit Python durchgeführt.