Model Reduction for Dynamical Systems SoSe 2015
Model Reduction for Dynamical Systems SS2014
| Lectures: | Office Hours: | on appointment | |
| Exercises: | Dr. Mian Ilyas Ahmad | Office Hours: | on appointment |
Schedule
| Lectures: |
Tuesday (every two weeks) Wednesday (every week) |
17:00 - 18:30 (1st Lecture on 07.04.2015) 09:15 - 10:45 |
G14-101 |
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| Exercises: | Tuesday (every two weeks) |
17:00 - 18:30 (1st Exercise on 14.04.2015) | G14-101 |
Lecture time shift in May!!!
The lectures on 19, 20 May will be shifted to 21, 22 May at 09:15-10:45.
The lecture room will be in MPI, the big seminar room V0.05-23.
Furtehr information
Contents
- Basics of linear systems and control theory.
- Model reduction methods for linear and nonlinear systems:
- modal truncation (eigenvalue-based methods),
- balanced truncation (SVD-based methods),
- Padé approximation / rational interpolation (Krylov subspace based methods),
- proper orthogonal decomposition (POD),
- dimension reduction via central/inertial manifolds (slow/fast decomposition)
- Applications of model reduction in computational science and engineering.
- Model reduction for parametric systems.
Certificate for successful participation
Kriterien zur Erlangung eines Leistungsnachweises:
- Mindestens 50% der Aufgaben sinnvoll bearbeitet.
- Mindestens zwei Aufgaben in der Übung vorrechnen.
Weitere Abschlussmöglichkeiten werden in der Vorlesung noch bekanntgeben.
References
- A.C. Antoulas: Approximation of Large-Scale Dynamical Systems, SIAM, Philadelphia, 2005.
- P. Benner, V. Mehrmann, D.C. Sorensen: Dimension Reduction of Large-Scale Systems, Springer-Verlag, Berlin/Heidelberg, June 2005.
- P. Benner, M. Hinze, E.J.W. ter Maten: Model Reduction for Circuit Simulation, Springer-Verlag, 2011.
- P. Benner: Numerical Linear Algebra for Model Reduction in Control and Simulation, GAMM Mitteilungen, 2006.
- R.W. Freund: Model reduction methods based on Krylov subspaces, Acta Numerica, 2003.
- G. Obinata, B.D.O. Anderson: Model Reduction for Control System Design, Springer-Verlag, 2000.
- W.H. Schilders, H.A. van der Vorst, J. Rommes Model Order Reduction: Theory, Research Aspects and Applications, Springer-Verlag, 2008.
- P. Benner Model Reduction for Linear Dynamical Systems, Summer School on Numerical Linear Algebra for Dynamical and High-Dimensional Problem, 2011.
Exercises
Exercise 1 Homework 1 dom_md_c.mat
Exercise 3 Homework 3 beam.mat
Exercise 4 Homework 4 CDPlayer.mat
Exercise 5 Homework 5 (No class on 9 June. The class is rescheduled to 11 June 2015 from 9:00 to 10:30 am in MPI, the big seminar room V0.05-23)
Exercise/Homework 7 Thermal.mat
Lectures
Lecture 1 Lecture 2/3 Lecture 4 Lecture5/6