Center for Optimization and Approximation (OA)

About us

The central tasks of our research in Optimization and Approximation are concerning simulation and optimization of economical and technical systems, as they are described by large systems of ordinary and partial differential equations. Our particular focus is on the transition from model-based simulation to model-based design. The wide spectrum of our activities ranges from theoretical investigations, through application-oriented research, to the numerical simulation and optimization of relevant practical topics.

Our current research activities include the following topics.

• Optimization of complex systems, which in general are described by systems of ordinary and partial differential equations, with applications to optimization of crystal growth, fluid-structure interactions, and applications to the nano sciences.
• Development, implementation and numerical analysis of structure exploiting finite element schemes in pde constrained optimization in the presence of control and state constraints.
• Development of tailored optimization methods for finite and infinite dimensional large-scale optimization problems, where non-smooth problems are of particular interest.
• Theory and numerical analysis of optimal control problems with applications to aerospace industry, fluid mechanics, vehicle dynamics, robotics, chemical engineering, and models from economics.
• Development of techniques for model reduction and data compression to describe, simulate and optimize ultra-large systems with applications to chip design, and for approximation of digital images and signals.
• Development and analysis of multilevel approximation methods using radial basis functions, splines, and wavelets for the numerical simulation of multiscale phenomena in time-dependent evolution processes, for the multiresolution representation of geometrical objects, and for efficient coding of digital images and signals.
• Design of numerical approximation algorithms for interdisciplinary problems arising from science and engineering and from industrial applications, such as in computer-aided design (CAD) and for the numerical simulation of multi-phase flow in industrial hydrocarbon exploration.
• Applications of numerical linear algebra to non-commutative problems, especially quaternions.

As for teaching, we offer courses on optimization, approximation, and numerical simulation on a regular basis for the diverse Bachelor, Master and Diploma Programmes of the Department of Mathematics. Moreover, basic courses on numerical analysis for students of mathematics as well as analysis courses for students of engineering at the Harburg University of Technology are jointly organized with the centre of differential equations and dynamical systems (DD).