Model Reduction of Dynamical Systems (Summer term 2019)
This course deals with Model Order Reduction (MOR) for the efficient simulation of large-scale dynamical systems.
Almost all MOR methods will be introduced and discussed, including both frequency domain and time domain methods: Balanced truncation, moment-matching, rational interpolation, POD, reduced basis method. MOR methods applied to real world problems will be presented in order to highlight the necessity and usefullness of model reduction.
Schedule
| Lectures: | ||
| Wednesday | 09:00 - 11:00 | G02 - 20 |
| Friday | 13:00 - 15:00 | G02 - 20 |
| Exercises: | Every second Wednesday/Friday at the same timings as Lectures (will be announced) | G02 - 20 |
Schedule announcements
- Next Exercise on : 10.04.2019 (Wednesday)
- On 24.04.2019 (Wednesday) there will be Lecture, On 26.04.2019 (Friday) there will be Exercise
- There will be no Lecture/Exercise On 08.05.2019 and 10.05.2019
Lectures
- Lecture 1 (Introduction)
- Lecture 2 (Mathematical basics I)
- Lecture 3 (Mathematical basics II)
- Lecture 4 (Mathematical basics III)
- Lecture 5 (Mathematical basics IV)
- Lecture 6 (Balanced truncation)
- Lecture 7 (Moment Matching)
- Lecture 8 (Nonlinear Model Order Reduction)
- Lecture 9 (Parametric Model Order Reduction (PMOR) - Linear systems)
- Lecture 10 (Parametric Model Order Reduction (PMOR) - Nonlinear systems)
Exercises
Homeworks
Contents
- Basics of linear systems and control theory.
- Model reduction methods for nonparametric linear and nonlinear systems:
- balanced truncation (SVD-based methods),
- Padé approximation / rational interpolation (Krylov subspace based methods),
- proper orthogonal decomposition (POD).
- Model reduction for parametric systems (multi-moment matching, reduced basis method).
- Applications of model reduction in computational science and engineering.
Certificate for successful participation
Criteria for getting a certificate for successful participation:
- Reasonable execution of at least 50% of the homework exercises.
- Demonstration of at least two homework exercises in the tutorial class.
Further information on exams will be given in the lecture.
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.