In its research profile, the research area Industrial Mathematics (Technomathematics) focuses on the modelling, analysis and numerical simulation of differential equations, and also on their optimization and control.

Technomathematics, as an important branch of applied mathematics, takes on problems from physics, engineering sciences or life sciences and develops models and techniques to deal with these issues in an analytical and numerical way. The research topics are highly application-oriented and partly influenced by current issues of the departments of the Fraunhofer ITWM. Thus, the developed mathematical methods and algorithms are immediately used to successfully address industry-related problems.

The mathematical competences of the research focus Technomathematics are to be found in the modelling, analysis and simulation with (stochastic) partial differential equations and differential algebraic equations, which will be applied in fluid dynamics, life sciences, radiation transport, transportation modelling and in the field of semigroup equations. Apart from the classical elliptic, parabolic and hyperbolic equations, stochastic differential equations as well as kinetic models and non-local integro-differential equations are analysed in the field of technomathematics, too. Other than that, methods from the optimization employing differential equations are used to solve the inverse problems and the optimal control problems of the foregoing fields of application. Through this field, there is a close cooperation with the branches of the algebraic and numeric control theory, which is applied in electrical engineering and vehicle simulation. The close cooperation of all the professors who have a share in this research area, be it through the fields of application or else the mutual influence of the research topics, generates synergies that guarantee the transfer of new mathematical methods into the departments of the Fraunhofer ITWM, and it also ensures being successful when filing an application for coordinated research projects together.