1. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 Course on Model Order Reduction Eindhoven, April 10-12, 2006

2. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 Organized by…. Centre for Analysis, Scientific Computing and Applications

3. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 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. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 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 preserving their input-output behavior. system inputoutput

5. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 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. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 Synonyms Model Order Reduction Reduced Order Modelling Behavioral Modelling Dimension Reduction of Large- Scale Systems ……………

7. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 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. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 Websites http://www.lc.leidenuniv.nl/lc/web/2 005/160/info.php3?wsid=160 (Workshop Model Order Reduction, Coupled Problems and Optimization)http://www.lc.leidenuniv.nl/lc/web/2 005/160/info.php3?wsid=160 http://web.mit.edu/mor/ (Model Order Reduction website at MIT)http://web.mit.edu/mor/ http://www.imtek.de/simulation/ind ex.php?page=http://www.imtek.uni- freiburg.de/simulation/benchmark/ (Oberwolfach Model Reduction Benchmark Collection)http://www.imtek.de/simulation/ind ex.php?page=http://www.imtek.uni- freiburg.de/simulation/benchmark/

9. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 More links Model order reduction page at Institut für Automatisierungstechnik, University of Bremen.Model order reduction page A very big collection of control-related aricles and theses of the Control Group at the University of Cambridge, UK.control-related aricles and theses Collection of the Model Order Reduction benchmarks for linear and nonlinear problems at the University of Freiburg, Germany.Collection of the Model Order Reduction benchmarks Another benchmark collection for model reduction from the Niconet web site.benchmark collection for model reduction Course material for "Dynamic systems and control" (6.241) course at MIT; essential for understanding dynamic systems theory.Course material for "Dynamic systems and control" ……and many others

10. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 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. © CHAMELEON RF 2005Model Order Reduction - Eindhoven – April 10-12, 2006 Enjoy the course! Jan ter Maten (COMSON) Siep Weiland (PROMATCH) Wil Schilders (CHAMELEON RF)