Mathematics

Analysis – Numerical Analysis – Optimisation encompasses several working groups on both campuses. The focus is on a broad range of themes, from theoretical questions on partial differential equations (variation problems, regularity theory, wave propagation, evaluation equations) to applications in mathematical physics, electrodynamics, optimisation and energy technology, image processing and numerical simulations in mechanical engineering, biomechanics and medicine.
The following projects are supported by the DFG (each with at least one paid position and material expenses):

• Singular variation problems and partialdifferential equations (working group of Prof. Ulrich Dierkes)
• Adaptive finite elements for parabolic equations (working group of Prof. Kunibert Siebert)
• Digital image processing using shearlets (working group of Prof. Gerlind Plonka-Hoch)
• Modelling and numerical simulation of artery walls (working group of Prof. Axel Klawonn)
• Participation in DFG Priority Programme 1324: “Mathematical methods for extraction of qualifiable information from complex systems” (working group of Prof. Gerlind Plonka-Hoch)
• Participation in DFG Priority Programme 1253: “Optimization with partial differentialequations” (working groups of Arnd Rösch, Rüdiger Schultz, Kunibert Siebert and former Professors Sergio Conti and Martin Rumpf. As such Duisburg-Essen has assumed a leading role in this particular area).

Other projects include cooperation withpartners in business and industry on interdisciplinary topics in optimisation / energy (E.ON) (working group of Prof. Rüdiger Schultz) and scheduling (Thyssen Krupp Steel and ifb AG) (working group of Prof. Günter Törner), and participation in the BMBF-sponsored network, “Basic research of renewable resources andrational energy use”.
In 2008, the Faculty of Mathematics began preparing its application for a Research Training Group in Analysis – Numerical Analysis – Optimisation. This will involve the working groups of Ulrich Dierkes, Axel Klawonn, Markus Kunze, Gerlind Plonka-Hoch, Arnd Rösch, Kunibert Siebert, Rüdiger Schultz, Michael Winkler, junior researcher Ruben Jacob and the successors to Professors Sergio Conti, Heinz-Dieter Nießen and Norbert Weck. The Group will look at theoretical and numerical questions of partial and standard differential equations as well as interdisciplinary approaches to simulation, modelling and optimisation in the aforementioned applications.
The department is already participating with three proposals in the DFG SPP / S23.
Scientists working in Analysis – Numerical Analysis – Optimisation helped organise conferences for the Society for Applied Mathematics (GAMM) in Bremen, the German Mathematicians’ Association (DMV) in Erlangen and the International Summer School held under the TopMath elite study programme.
Stefanie Tenorth received the prize of the German Mathematicians’ Association (DMV) for her thesis on “Generalized Rudin-Osher-Fatemi Regularization for Signal Interference Suppression”. Kristin Kohls received the Alumni Prize from the University of Augsburg, and Oliver Rheinbach the ECCOMAS (European Community on Computational Methods in Applied Sciences) Award for the best dissertation of 2007.