Course on Model Order Reduction

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# Course on Model Order Reduction - PowerPoint PPT Presentation

Course on Model Order Reduction Eindhoven, April 10-12, 2006 Organized by…. Centre for Analysis, Scientific Computing and Applications Model Order Reduction? Obtain a compact description of behavior by reducing the complexity of the model, using only the dominant part of the behavior

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## Course on Model Order Reduction

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Course onModel Order Reduction

Eindhoven, April 10-12, 2006

Organized by….

Centre for Analysis, Scientific Computing and Applications

Model Order Reduction?

Obtain a compact description

of behavior by reducing the complexity of the

model, using only

the dominant part of the behavior

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

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

### Enjoy the course!

Jan ter Maten (COMSON)

Siep Weiland (PROMATCH)

Wil Schilders (CHAMELEON RF)