Teams
Model Order Reduction (MOR)
In order to get a deep insight into the underlying process, dynamics, structure or devices, modeling and simulation are unavoidable in many research and application fields. The resulting mathematical models are usually in the form of partial differential equations. To simulate such models, spatial (-time) discretization is necessary, which results in large-scale, complex systems with enormous number of equations. The simulation becomes time-consuming because of the large scale and complexity of the systems.
Computer Aided Control System Design (CACSD)
Computer aided control system design refers to numerical methods for the design of controllers and on modeling, discretization, and simulation of systems with controls and observations. The work on effective control setups combines methods from the fields of model order reduction, matrix equations, and scientific computing.
Numerical Linear and Multilinear Algebra (NLMA)
We study numerical methods for linear and nonlinear eigenvalue problems. This includes the development and analysis of new algorithms, (backward) error analysis, and the derivation of the associated (relative) perturbation theory. Special attention is given to linear, generalized, and polynomial eigenproblems with spectral symmetries.
Moreover, we investigate the solution of special linear systems of equations arising in PDE control and model reduction algorithms.
Moreover, we investigate the solution of special linear systems of equations arising in PDE control and model reduction algorithms.
Scientific Computing (SC)
Scientific Computing is an interdisciplinary field of research including Mathematics, Computer Science, and Application Sciences, where researchers of all fields jointly work on the computer based solution of active applications. Besides the cassical questions of parallel implementation, energy-aware formulations of all kinds of computational methods and exploitation of special purpose low power hardware are becoming more and more important.
Simulation of Energy Systems (SES)
Modeling and simulation of fluids in large networks is a challenging problem, especially if the simulation is used to provide solutions to optimal control problems or other optimization questions. Our first goal is to be able to simulate this systems in a stable and efficient manner as truely transient systems, considering in particular the underlying network stucture.
Matrix Equations (ME)
Nearly all other research fields of the CSC group involve matrix equation computations at a certain point. The work of this team is dedicated to the efficient numerical solution of the variety of those equations in all kinds of working environments.