Professur Wissenschaftliches Rechnen
Wissenschaftliches Rechnen
Professur Wissenschaftliches Rechnen 

Winter Semester 2019/20

Model Order Reduction (3V + 1Ü)

Lecture: Martin Stoll & Dominik Garmatter

Exercise: Dominik Garmatter

News

  • The seventh Exercise sheet is online.
  • The Lecture notes are online. This is a preliminary version and will be adjusted and corrected throughout the lecture period.
  • Depending on the participants of the course, the lectures and exercise groups will be held in English or German.
  • The first lecture will be on Monday, 14th of October, 4. LE (13:45 - 15:15) in room 2/B202.
  • On Tuesday, 15th of October, 5. LE (15:30 - 17:00) in room 2/B202, there will be a preliminary exercise concerning questions. The first real exercise will be two weeks later.
  • Any questions can be directed to Dominik Garmatter.

Content of the course

The course will consist of two parts. The first part will be an introduction to Reduced Basis Methods for elliptic partial differential equations. Numerical methods for the solution of such equations usually result in high-dimensional and thus computationally demanding problems. This becomes especially troublesome, if the the discretized problems need to be solved numerous times, e.g. for a varying paramter, and this becomes relevant in the context of parameter identification, optimization or design. Reduced Basis Methods allow for an efficient treatment of such parametric problems The key ingredients of the method are: construction of low-dimensional approximation spaces (reduced basis spaces) via so-called snapshots, Galerkin projection of the problem onto the reduced basis space and an efficient implementation of the scheme which allows for a rapid solution and thus parameter variation. The second part of the course will then investigate model order reduction techniques for Linear Time Invariant (LTI) systems where the method of Balanced Truncation will be the focus.

Dates

Lectures
  • Monday, 4. LE (13:45 - 15:15), room 2/B202
  • Tuesday, 5. LE (15:30 - 17:00), room 2/B202 (every second week, interchaning with the exercise course)
Exercise
  • Tuesday, 5. LE (15:30 - 17:00), room 2/B202 (every second week, interchaning with the second lecture)
Add the course to your own schedule via

Keine Lehrveranstaltung gefunden.

Prerequisites

  • Basic knowledge of numerics of PDEs, programming knowledge in Matlab.
  • The lecture "Numerik partieller Differentialgleichungen" is NOT required.

Material

Script
  • Lecture notes (preliminary version, will be adjusted and corrected throughout the lecture period)
Exercise
  • Exercise sheet 1
  • Exercise sheet 2
  • Exercise sheet 3
  • Exercise sheet 4
  • Exercise sheet 5
  • Exercise sheet 6
  • Exercise sheet 7
RBmatlab
  • Zip-file (approx 200 MB); alternatively see MoRePaS regarding the download and Introduction for an installation guide.

Exam

  • The exam will consist of a 30-minute oral exam.
  • Exam dates can made in consultation with Dominik Garmatter towards the end of the lecture period.

Modul Affiliation

  • "Forschungsmodul Numerische Mathematik" (FN2) and "Forschungsmodul Angewandte Mathematik" (FM2).

Literature

  • D. Braess, Finite Elemente, Springer, 2013.
  • H.W. Alt, Lineare Funktionalanalysis, Springer, 1992.
  • Rozza, G., Huynh, D. B. P., and Patera, A. T. (2007), Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations, Archives of Computational Methods in Engineering, 15(3), 2007.
  • A.C. Antoulas, Approximation of Large-Scale Dynamical Systems, SIAM, 2005.