Martin Pieper

Vector hyperinterpolation on the sphere

We present new results on hyperinterpolation for spherical vector fields. Especially we consider the operator Ln, which may be described as an approximation to the L2 orthogonal projection Pn. In detail, we prove that Pn is the projection with the least uniform norm and that Ln has the optimal value for its norm in the C→L2 setting. These results are already known for the scalar case. In the continuous space setting, we could prove only a sub-optimal bound for the Lebesgue constant of the vector hyperinterpolation operator.

Nonlinear integral equations for an inverse electromagnetic scattering problem

We present a new method to solve an inverse scattering problem for time-harmonic electromagnetic waves. The method is based on an equivalence relation of the inverse problem to a system of two integral equations. This system can be solved numerically by a recently developed spectral method for the direct scattering problem.

Theoretische Grundlagen der Optimierung

Wir befassen uns in diesem Kapitel mit der Optimierungstheorie. Wir beginnen mit Optimierungsproblemen ohne Nebenbedingungen und geben die allgemeine, mathematische Formulierung des Problems an. Anschliesend diskutieren wir die Optimalitatsbedingungen erster und zweiter Ordnung, mit deren Hilfe wir Minima der Zielfunktion bestimmen konnen. Im nachsten Abschnitt nehmen wir dann Nebenbedingungen hinzu, die durch Gleichungen und Ungleichungen formuliert werden. Als Optimalitatskriterien werden wir den Satz von Karush, Kuhn und Tucker (KKT) kennen lernen.

Biogas Production Modelling: A Control System Engineering Approach

Due to the Renewable Energy Act, in Germany it is planned to increase the amount of renewable energy carriers up to 60%. One of the main problems is the fluctuating supply of wind and solar energy. Here biogas plants provide a solution, because a demand-driven supply is possible. Before running such a plant, it is necessary to simulate and optimize the process feeding strategy. Current simulation models are either very detailed like the ADM 1, which leads to very long optimization runtimes or not accurate enough to handle the biogas production kinetics. Therefore this paper provides a new model of a biogas plant, which is easy to parametrize but also has the needed accuracy for the output prediction. It is based on the control system approach of system identification and validated with laboratory results of a real biogas production testing facility.