Model Reduction for Dynamical Systems SS2012
|Lectures:||Prof. Dr. Peter Benner||Office Hours:||on appointment|
|Exercises:||Tobias Breiten||Office Hours:||on appointment|
Schedule - Further Information - Contents - Certificates - References - Exercises - Lecture material
|Lectures:||Thursday,||01:00 pm - 03:00 pm (1. Lecture on 04/12/2012)||V0.05-2+3 (MPI)|
|Exercises:||Tuesday,||11:00 am - 01:00 pm (1. Exercise on 04/24/2012)||V0.05-2+3 (MPI)|
- Course description.
- Important: Lecture instead of exercise session on April 17, 2012!
- Important: no lecture/exericse session on June 19/21, 2012!
- 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.
- 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.
- Exercise 1, dom_md_c.mat (compressed dom.tar)