Center for Optimization and Approximation (OA)
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
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
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,
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).