**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.

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.