Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-81-39-M-7

Model Order Reduction for Large Scale Systems (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-39-M-7 Model Order Reduction for Large Scale Systems 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-81-39-K-7
Model Order Reduction for Large Scale Systems
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-81-39-K-7]: Title: "Model Order Reduction for Large Scale Systems"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86314 ("Model Order Reduction for Large Scale Systems")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Model reduction methods for ordinary and partial differential equations are discussed, in particular
  • Krylov space methods,
  • reduced bases,
  • Proper Orthogonal Decomposition (POD).

Competencies / intended learning achievements

By completing this module, the students know and understand basic concepts for theoretical and numerical model order reduction of large scale systems. They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and are able to reproduce and explain them. In particular, they can outline the conditions and assumptions that are necessary for the validity of the statements.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and methods taught in the lecture. They have learnt how to apply the methods to new problems, analyze them and develop solution strategies.

Literature

  • A.C. Antoulas: Approximation of Large-Scale Dynamical Systems,
  • A.T. Patera and G. Rozza, Reduced Basis Approximation and A Posteriori Error Estima-tion for Parametrized Partial Differential Equations,
  • P. Benner, V. Mehrmann, D.C. Sorensen: Dimension Reduction of Large-Scale Systems,
  • W.H. Schilders, H.A. van der Vorst, J. Rommes: Model Order Reduction: Theory, Re-search Aspects and Applications.

Materials

Further literature will be announced in the lecture.

References to Module / Module Number [MAT-81-39-M-7]

Module-Pool Name
[MAT-81-MPOOL-7] Specialisation Partial Differential Equations (M.Sc.)
[MAT-82-MPOOL-7] Specialisation Systems and Control Theory (M.Sc.)
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)