Course on Model Order Reduction

1. Course onModel Order Reduction Eindhoven, April 10-12, 2006

2. Organized by…. Centre for Analysis, Scientific Computing and Applications

3. Model Order Reduction? Obtain a compact description of behavior by reducing the complexity of the model, using only the dominant part of the behavior

4. Model Order Reduction? Model Order Reduction (MOR) is a branch of systems and control theory, which studies properties of dynamical systems in application for reducing their complexity, while preservingtheir input-output behavior. system input output

5. Goals and problems of Model Order Reduction • To make a reduction process automatic (the algorithm doesn't know anything about the nature of underlying system) • Sometimes we need to preserve some system properties, such as passivity, stability, etc. • To ensure good approximation of the original system by the reduced system in various aspects • Maybe we may vary some parameter of a system (i.e. length of transmission line). We need to be able to create parametrized reduced models. • Since non-reduced models may have millions of unknowns, the algorithm must be efficient.

6. Synonyms • Model Order Reduction • Reduced Order Modelling • Behavioral Modelling • Dimension Reduction of Large-Scale Systems • ……………

7. Books • P. Benner, V. Mehrmann, D. Sorensen, “Dimension Reduction of Large-Scale Systems” (2005) • A. Antoulas, “Approximation of Large-Scale Dynamical Systems” (2005) • B. N. Datta, “Numerical Methods for Linear Control systems“ (2004) • G. Obinata, B. D. O. Anderson, “Model Reduction for Control System Design” (2004) • Z. Q. Qu, “Model Order Reduction Techniques with Applications in Finite Element Analysis” (2005) • H.A. van der Vorst, W.H.A. Schilders, “Model Order Reduction: Theory and Practice” (to appear)

8. Websites • http://www.lc.leidenuniv.nl/lc/web/2005/160/info.php3?wsid=160 (Workshop “Model Order Reduction, Coupled Problems and Optimization”) • http://web.mit.edu/mor/ (Model Order Reduction website at MIT) • http://www.imtek.de/simulation/index.php?page=http://www.imtek.uni-freiburg.de/simulation/benchmark/ (Oberwolfach Model Reduction Benchmark Collection)

9. More links • Model order reduction page at Institut für Automatisierungstechnik, University of Bremen. • A very big collection of control-related aricles and theses of the Control Group at the University of Cambridge, UK. • Collection of the Model Order Reduction benchmarks for linear and nonlinear problems at the University of Freiburg, Germany. • Another benchmark collection for model reduction from the Niconet web site. • Course material for "Dynamic systems and control" (6.241) course at MIT; essential for understanding dynamic systems theory. • ……and many others

10. This course • Will provide a thorough introduction to Model Order Reduction • Starts with Basic Concepts in numerical linear algebra and systems&control • Treats the linear case extensively, demonstrating different methods (Krylov based, Gramian based, POD) • Discusses current research (nonlinear MOR, parametrized MOR) • Several applications will be shown • And hands-on experience with a variety of methods and software tools

11. Enjoy the course! Jan ter Maten (COMSON) Siep Weiland (PROMATCH) Wil Schilders (CHAMELEON RF)