Research Groups in Applied Mathematics

 

Optimization and Approximation
Professors:
Prof. Dr. K. Klamroth
Prof. Dr. M. Heilmann
Apl. Prof. Dr. P. Beisel
Apl. Prof. Dr. M. Mendel

Description:

Mathematical optimization is a thriving and innovative branch of mathematics with a high application potential in economics, engineering and life sciences. Examples include, but are not limited to, applications in logistics (e.g., supply chain management), production (sequencing and scheduling), location planning, portfolio optimization, routing problems and automated robot control as well as optimization problems occuring in biology and medical sciences as, for example, medical image registration.

The focus of our work is on discrete and discrete-continuous optimization problems, including modelling issues, theoretical analysis and the development of solution methods in an application oriented context. The solution of discrete optimization problems is typically highly complex, and the development of efficient and reliable solution methods is still a big challenge (many practical optimization problems can, despite the fast development of computer technology, so far not be solved exactly). Scientific progress in this field is thus of high theoretical and practical relevance.

Approximation theory deals with the replacement of complicated mathematical objects with more easy-to-handle ones, keeping the problem's primal information content. Examples include questions of existence, uniqueness and characterization of best approximating elements, the study of the relationship between quality of approximation and structural properties of the approximated objects, and the analysis and application of concrete approximation methods.

To the research group homepage Back to the overview page

 

Numerical Analysis
Professors:
Prof. Dr. M. Günther (Head of Research Group)
Prof. Dr. M. Ehrhardt
Prof. em. Dr. S. Schlosser-Haupt (Professor emeritus)
Prof. em. Dr. G. Heindl (Professor emeritus)

Description:
The progress in data processing over the last forty years has opened all new application areas to mathematics and demands its continuous development as a modern science. A close, natural interaction of mathematics, engineering, and computer science emerged and has settled in a new discipline, scientific computing. Today, the traditional engineering and natural sciences problems are supplemented by an increasing number of tasks from economy and social sciences.

The economic impact of scientific computing is briefly highlighted by slogans such as "high-tech equals math-tech" or "high technology equals mathematical technology".

Besides the classical dichotomy, theory and experiment, here simulation offers a third access to knowledge, and is already indispensable for technological progress. So, the specification of this task is precisely defined by the Association of Engineers (VDI) in Norm 3633. It can be concisely stated as: Simulation is the reproduction of a system and its dynamic processes in an experimental model to achieve knowledge which carries over to reality.

Real objects and their interrelations are replaced by mathematical models. These are tested and experienced: simulation is experimentation with models. In an industrial environment, simulation replaces the time and cost consuming real, physical experiments by computer tasks.

Our research group represents and considers numerical analysis as the core part of scientific computing. The main objective of numerical analysis is the development, analysis and implementation of efficient and robust numerical algorithms to simulate mathematical models. The analytical properties of mathematical models affect this task as well as the hard- and software implications of underlying computer environments; both have to be included to the method's development. In the context of scientific computing, numerical analysis is per se interdisciplinary.

For more detailed informations concerning the activities of our research group, please refer...

To the research group homepage Back to the overview page

 

Stochastics / Statistics
Professors:
Prof. Dr. B. Rüdiger-Mastandrea (Head of Research Group)
Prof. Dr. F.R. Diepenbrock

Back to the overview page