The Weierstrass Institute conducts project oriented research in applied mathematics with the aim of solving complex problems in technology, science and the economy. The institute deals with the whole scientific solution process, starting with mathematical modeling, followed by the theoretical analysis of models, and ending with the numerical simulation of the solution. In this context, the WIAS maintains long term, wide-ranging contacts with those who apply mathematics in industry and other areas of research and for whom it is a reliable partner.
The institute’s core strengths are applied analysis and stochastics, developing and implementing numerical algorithms, and producing scientific software, as well as the consistent mathematical modeling of scientific and technological phenomena, and suitably combining all these strengths. Due to this wide range of strengths, WIAS is able to work on complex problems over long periods of time and through different phases, as well as tackle new problems and deliver fast solutions.
Application areas are oriented towards social requirements like the utilization of energy, development of medicine, research on material characteristics, or the quality analysis of technological innovations. One of these application areas is Nano- and Optoelectronics.
Optical technologies are one of the most important future-oriented industry of the 21st century, contributing significantly to technological progress. They facilitate innovative infrastructures, which are indispensable for further digitalization of industry, science, and society.
Mathematical modeling, numerical simulation, as well as theoretical understanding of the occuring effects are important contributions of WIAS to today’s technological challenges. A central topic is the modeling and mathematical analysis of the governing equations and the simulation of semiconductor devices.
Core areas are:
- organic semiconductors (e.g. organic light-emitting diodes)
- applications of laser technologies and problems of nonlinear fiber optics
- mathematical optimization of opto-electronic devices (silicon photonics)
- quantum-mechanical modeling of nano-structures and their consistent coupling to macroscopic models
- hybrid modeling of semiconductor devices and “bulk-interface” processes
- efficient algorithms in diffractive optics for the simulation of scattering on novel nano-structured surfaces