The Research Training Group 1294 of the German Research Foundation (DFG)
- "Analysis, Simulation and Design of Nanotechnological Processes"
is organized by scientists of the Reseach Focus on Partial Differential Equations the Department of Mathematics at the Karlsruhe Institute of Technology.
The Research Training Group aims to investigate physical models in nanotechnology (in particular in optics and photonics) with the means of modern mathematics, to analyze the resulting equations, and to devise novel methods for their numerical simulation. Within this field of research, a broad scope of different topics will be tackled. For example, the existence and stability of spatially localised light pulses in periodic and perturbed periodic materials is supposed to be established. A similar analysis will be carried out for standing waves in nonlinear materials. In many applications the optical parameter of the given material are not known and can only be determined indirectly from measurements of the scattered field. This calls for sophisticated methods for parameter identification. To simulate optical devices (such as photonic crystals, ring resonators, metamaterials) in realistic situations, efficient software tools have to be developed. Algorithms and strategies of mathematical optimisation will be used to make the systematic design of new devices possible. The successful treatment of these problems requires a variety of methods ranging from mathematical modelling via the analysis and numerics of partial differential equations to the theory of inverse problems and optimisation. The research training group thus provides a rich concept for interdisciplinary qualification.