Mathematics

The research centre for Analysis/Numerics/Optimisation consists of several research groups located on both campuses. The variety of research topics is broad, ranging from analysis of partial differential equations to numerical simulation and optimisation. The application background of these research topics is in geometrical problems, biomechanics, energy management, fluid dynamics, synthesis of microstructures and dynamic systems.
New appointments were made to three chairs in Analysis in the last two years, with three excellent scientists in Professor Petra Wittbold, Professor Andreas Gastel and Professor Patrizio Neff joining the Faculty.
Three projects of the Arnd Rösch, Rüdiger Schultz and Kunibert G. Siebert research groups 
are participating in the second phase of the DFG Priority Programme 1253 “Optimisation with Partial Differential Equations”. This underlines the leading position of our Faculty in this research area. The approved research projects are  “Numerical analysis and discretization strategies 
for optimal control problems with singularities” (Professor Arnd Rösch together with Professor Thomas Apel and Professor Boris Vexler), 
“Multi-Scale Shape Optimization under Uncertainty” (Professor Rüdiger Schultz together with Professor Sergio Conti and Professor Martin Rumpf) and “Design and Analysis of Adaptive Finite Element Discretizations for Optimal Control Problems” (Professor Kunibert G. Siebert, Professor Arnd Rösch).
Above and beyond these, the following projects are being funded by the German Research Foundation (DFG): “Adaptive Finite Elements for Parabolic Equations” (Professor Kunibert G. Siebert), “Bubbling off” phenomena for conform invariant functionals of higher order (Professor Andreas 
Gastel), “Singular geometric variational problems and partial differential equations” (Professor Ulrich Dierkes), and “Massive parallel simulation of arterial walls: Modelling and numerical solution via FETI domain decomposition methods” (Professor Axel Klawonn together with Professor Jörg Schröder).
The work of Professor Rüdiger Schultz’ research group on optimisation for power networks was extended to include new research topics. 
A network project funded by the BMBF on renewable energy and rational energy consumption and a project supported by BMWi and MAN Turbo Oberhausen to integrate a fully automatic optimisation function for compressor controls were successfully completed. A new field of application was also added in the optimisation of gas transport in pipeline systems. Here, the working group of Professor Rüdiger Schultz is cooperating with the gas transport corporation Open Grid Europe from Essen to investigate the technical capacities of gas networks with the support of the BMWi and the Federal Network Agency.
Simulations on parallel computers with several tens or even hundreds of thousands of processors or kernels require scalable algorithms if the performance of such computers is to be exploited to optimal effect. The Chair of Numerical Mathematics on the Essen Campus develops scalable domain decomposition methods for this type of computer. The algorithms are also used for the new supercomputer JUGENE located at the Forschungszentrum Jülich research centre. With almost 300,000 kernels, this computer is currently Number 9 in the Top 500 of the world’s fastest computers. In July 2010, the University unveiled a new Cray XT6m with over 4000 processor kernels. This computer was financed through the DFG on the basis of an application in which the Klawonn research group was also involved and with financial contributions from various faculties, the Universiy and the ZIM. The Collaborative Research Centre SFB-TR45 was another financial contributor for Mathematics. One of the uses of the computer is for the simulation of arterial walls as part of a long-standing, DFG-funded cooperation between engineering and medicine with Professor Jörg Schröder from the Faculty of Engineering and Professor Raimund Erbel from the West German Tumour Centre of University Hospital Essen. The group of Axel Klawonn, Oliver Rheinbach and Stephanie Vanis is also working with the research group of Patrizio Neff on the numerical simulation of micromorphic elasticity problems.
The new working group of Professor Michael Winkler intensified the international nature of its research in cooperation with universities in Paris (Paris 13), Madrid (Universidad Autonoma and Universidad Politecnica) and Warsaw. A guest professorship of Professor José Ignacio Tello (Madrid) at the University in 2010 was also financed by the DFG.

Research collaborations:

• Prof. Thomas Apel (Universität der Bundeswehr München)
• Dr.-Ing. Daniel Balzani (Caltech, USA)
• Dr. Simone Deparis (Ecole Polytechnique de Lausanne, Switzerland)
• Dr. Clark Dohrmann (Sandia National Laboratories, Albuquerque, USA)
• Prof. Dr. med. Raimund Erbel (Westdeutsches Herzzentrum, Essen)
• Prof. Marek Fila (Univerzita Komenskeho, Bratislava, Slovakia)
• Prof. Roland Herzog (TU Chemnitz)
• Dr. Marta Jarosova (TU Ostrava, Czech Republic)
• Prof. Philippe Laurencot (Universite Toulouse, France)
• Prof. Christian Meyer (TU Darmstadt)
• Prof. Pedro Morin (Universidad Nacional del Litoral, Argentina)
• Prof. Ricardo H. Nochetto (University of Maryland, USA)
• Prof. Georg Pflug (Uni Vienna)
• Prof. Andrzej Ruszczynski (Rutgers University)
• Prof. Dr.-Ing. Jörg Schröder (Mechanics, University of Duisburg-Essen)
• Prof. Alex Shapiro (Georgia Institute of Technology)
• Prof. Philippe Souplet (Universite Paris 13, France)
• Prof. Endre Süli (Oxford University, England)
• Prof. J. IgnacioTello (Universidad Politecnica, Madrid, Spain)
• Prof. Juan Luis Vazquez (Universidad Autonoma, Madrid, Spain)
• Prof. Andreas Veeser (Universita degli Studi die Milano, Italy)
• Prof. Boris Vexler (TU München)
• Prof. Olof Widlund (Courant Institute, New York, USA)
• Prof. Dariusz Wrzosek (Universitas Vasoviensis, Warsaw, Poland)
• Prof. Eiji Yanagida (Tohoku University, Sendai, Japan).

Conference organisation

• Workshop: “Adaptive Finite Elements: Analysis und Applications”, 7–11 September 2009, Kirchzarten (Black Forest), partially supported by the DFG Research Unit “Nonlinear Partial Differential Equations” (Professor Kunibert G. 
Siebert together with Dr. Claus-Justus Heine and Professor Andreas Veeser)
• Summer School and Workshop: “Analysis and Numerics of PDE Constrained Optimization”, 19–23 July 2010, Lambrecht (Pfalz), supported by the DFG Priority Programme 1253 (Arnd Rösch, Rüdiger Schultz, Kunibert G. Siebert)
• Söllerhaus Workshop: “Domain Decomposition Methods for Heterogeneous Field Problems”, 2–6 June 2010, Hirschegg, Austria (Professor Klawonn together with Professors Ulrich Langer, Olaf Steinbach, Luca Pavarino and Olof Widlund).