Main Application Areas

Nano- and optoelectronics
Analysis, modeling, and simulation of semiconductor lasers, semiconductor nanostructures, and other optoelectronic components as well as of semiconductor manufacturing technologies.
Optimization and control of technological processes
Methods of PDE-constrained optimal control and control of differential algebraic equations are employed in a variety of applications.
Phase transitions and multi-functional materials
Many important industrial manufacturing processes (e.g., production and treatment of steel, growth of semiconductor crystals) rely on phase transitions. Hence, there is a special demand for their mathematical modeling and simulation.
Flow and transport problems in continua
Flow and transport of species are important in many processes in nature and industry. In general, they are modeled by systems consisting of partial differential equations.

Active fields of research are questions concerning the analysis, the numerical analysis, and the numerical simulation of partial differential equations from computational fluid dynamics (CFD). The considered applications include, for example, electrochemical systems, population balance systems and flows in porous media.
Conversion, storage and distribution of energy
Analysis, modeling, and simulation of different aspects of research on renewable energies as well as for the effective use of conventional energy resources.
Random phenomena in nature and economy
Modern statistical and probabilistic methods form the theoretical basis to model and analyze complex stochastic phenomena. WIAS has, with main mathematical contributions, become an authority in this field including its applications to problems in science, technology, medicine and environmental research as well as risk evaluation for financial products.