TU CE GSC CE People at the Graduate School CE Principal Investigators Jens Lang - Numerics of Partial Differential Equations

The research concerns the development of efficient and practical computational algorithms for the adaptive solution of partial differential equations (PDEs) arising in such fields as biology, chemistry, medicine, and combustion. Of particular interest are all aspects of adaptively generating a grid in space and time that evolves with the solution of the PDE. Another research topic is the design of higher-order linearly implicit time integrators of Rosenbrock-type which allow the efficient solution of very stiff equations. Adaptive methods have been applied successfully to real-life problems including, e.g., the simulation of two-phase bubble reactors, solid-solid alloying reactions, dopant diffusion in semiconductor device fabrication, regional hyperthermia of deep seated tumors, brine transport in porous media, and the heartbeat. Multi-physics problems such as fluid-solid interaction and radiative heat transfer have been considered. Special mesh adaptation strategies have been developed that have an enormous potential for problems where free surfaces appear or inner dynamic boundaries have to be resolved. In addition, hierarchical multi-scale modelling is used to reduce the complexity of challenging problems. Novel adjoint-based techniques have been investigated to control the model reduction process. The group is just progressing to optimization with PDEs. Attention is paid to optimal control and topology optimization problems as well. The aim is to explore and utilize specific mathematical structure of applications, structure exploiting algorithms, and adaptivity in optimization. For example, the solution of optimization and control problems for flow processes in gas and water networks is considered. Global solutions of corresponding optimization and control problems are obtained via a hierarchy of combinatorical and continuous methods.

Technische Universität Darmstadt

Graduate School CE

Dolivostraße 15

D-64293 Darmstadt

| |||||||

Fax | +49 6151/16-24404 | ||||||

Office | S4|10-322 |

Send e-mail to assistants' office

Show a list of open BSc/MSc topics at GSC CE.