Teaching Activities
Model Reduction for Dynamical Systems SS2014
| Lectures: | Dr. Lihong Feng | Office Hours: | on appointment |
| Exercises: | Dr. Mian Ilyas Ahmad | Office Hours: | on appointment |
Schedule - Further Information - Contents - Certificates - References - Exercises - Lecture material
Schedule
| Lectures: | Thursday | 1:00 pm - 3:00 pm (1st Lecture on 03.04.2014) | G14-101 | ||
| Exercises: | Tuesday, | 1:00 pm - 3:00 pm (1st Exercise on 04/08/2014) | G05-300 |
Notice:
Lectures on June 12 and June 26 fall out.
There will be Lectures on June 17 and June 30 as below.
| Lectures: | June 12 --> | June 17, 09:00 am - 11:00 am | V0.05-2+3 (MPI) | ||
| Lectures: | June 26 --> | June 30, 09:00 am - 11:00 am | V0.05-2+3 (MPI) |
Further 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
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.