Research Group "Numerical Mathematics and Scientific Computing"
Head:Volker John
Coworkers:
Gabi Blättermann, Jürgen Borchardt, Alfonso Caiazzo, André Fiebach, Jürgen Fuhrmann, Klaus Gärtner, Hartmut Langmach, Alexander Linke, Gerd Reinhardt, Volker Schloßhauer, Rainer Schlundt, Ellen Schmeyer, Swetlana Schyschlowa, Hang Si, Holger Stephan, Timo Streckenbach, Carina Suciu, Manfred Uhle, Hong Zhao
Secretary:
Marion Lawrenz
Apprenticeship Training : Mathematical-Technical Softwaredeveloper:
Apprentices: Adrian Lehmann and Joram Wittke
Training Supervisor: Gerd Reinhardt
Contact: Phone: +49 30 20372 566, Fax: +49 30 20372 317
The mathematical modeling of a large number of scientific and technical problems leads to systems of differential equations describing the interactions of temporal and spatial variations of the considered physical processes. If the spatial variations are irrelevant, the processes are described by ordinary differential equations (ODEs). The connection with additional algebraic equations results in differential-algebraic equations (DAEs). DAEs are used to model, e.g., electrical networks and chemical plants. If the spatial structure of the process is important, partial differential equations (PDEs) are used as models. PDEs describe problems from structural analysis, from fluid mechanics, electro-magnetic problems or particle diffusion. In general, it is not possible to solve the equations arising from applications in closed form. Numerical methods have to be used to obtain approximate solutions.
The research group develops, analyzes and implements modern numerical methods for the solution of systems of PDEs and DAEs. An essential aspect of the studied methods is their practicability in applications.
The emphasis of the research activities is on:
- finite element and finite volume methods for the spatial discretization of PDEs,
- implicit schemes for their temporal discretization,
- numerical methods for systems of DAEs and resulting questions of numerical linear algebra and
- computational geometry (grid generation).
The research group takes part in the following main application areas: