Model Reduction of Dynamical Systems (Summer Term 2017)
Schedule
| Lectures: | Monday (every two weeks), | 15:00 - 16:45 (from 03.04.2017), | G14-101 |
| Wednesday (every week), | 09:00 - 10:45, | G12-201 | |
| Exercises: | Monday (every two weeks), | 15:15 - 16:45 (from 10.04.2017), | G14-101 |
Changes to the schedule
- Lecture will replace exercise on 24.04.2017 (Monday).
- Exercise will replace lecture on 07.06.2017 (Wednesday).
- There will be no lectures on 12 and 14.06.2017. Instead, lecture will take place on 15 and exercise on 16.06.2017, 9:00 - 10:45, at Max Planck Institute (Sandtorstr. 1) in the big seminar room.
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 MOR)
- Lecture 9 (PMOR - Linear systems)
- Lecture 10 (PMOR - POD and Reduced basis methods)
Exercises
For opening and running Jupyter notebooks, you need a Python installation. You can use the Linux Virtual Machine (1.7 GB), or install Python on your own machine. Instructions are available as a Markdown file here.
- Exercise 1, Jupyter notebook
- Exercise 2, Jupyter notebook
- Exercise 3
- Exercise 4, Jupyter notebook
- Exercise 5, Jupyter notebook
- Exercise 6
- Exercise 7
- Exercise 8
Homeworks
- Homework 1 (Deadline: 05.05.2017)
- Homework 2 (Deadline: 19.05.2017)
- Homework 3 (Deadline: 02.06.2017)
Contents
- Basics of linear systems and control theory.
- Model reduction methods for nonparametric 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).
- 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.