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Model Order Reduction Techniques (Modellreduktionsverfahren)

Prof. Martin Grepl
Prof. Karen Veroy-Grepl


News

  • First meeting: Thursday, 20.04.2017, at 14:00pm in room 224.3 (main building).

  • Time of lectures to be discussed during the first meeting (if you are interested in the course but cannot attend the first meeting, please send us an email).


Dates

Course Dates Notes
Lecture Friday, 8:30 - 10:00 (room 224.3) Start: 28.04.2017
tbd Start:
Recitation Friday, 10:00 - 11:30 (biweekly)
Final Exam tbd

Course Description

The focus of this course is on model order reduction methods for large-scale systems. These systems typically arise when partial differential equations are solved using numerical methods such as the finite element method. Model order reduction techniques provide an efficient and reliable way of solving these problems in the many-query or real-time context, such as optimization, characterization, and control. We first present reduced basis approximations and associated a posteriori error estimation procedures for rapid and reliable solution of parametrized partial differential equations (PDEs). The focus is on rapidly convergent Galerkin approximations on a space spanned by "snapshots" on the parametrically induced solution manifold; rigorous and sharp a posteriori error estimators for the outputs/quantities of interest; efficient selection of quasi-optimal samples in general parameter domains; and Offline-Online computational procedures for rapid calculation in the many-query and real-time contexts. We subsequently consider Proper Orthogonal Decomposition (POD) and Balanced Truncation for the approximation of systems which only depend on time.

Reference Texts


Lecture Slides and Notes (will be posted before each lecture)

  • Lecture 1 (28.04.2017): Motivation and Introduction. (slides).
  • Lecture 2 (05.05.2017): General Preliminaries, Linear Elliptic Problems (Definitions, Truth Approximation, Reduced Basis Approximation). (slides or article ).
  • Lecture 3 (12.05.2017): slides/notes of Lecture 2
  • Lecture 4 (19.05.2017): slides/notes of Lecture 2
  • Lecture (26.05.2017): postponed
  • Lecture 5 (02.06.2017): A Posteriori Error Estimation for Linear Elliptic Problems. (slides or article).
  • Lecture 6 (16.06.2017): slides/notes of Lecture 5
  • Lecture 7 (22.06.2017): Convergence of RB Approximations. (slides or article).
  • Lecture 8 (23.06.2017): Noncompliant Linear Elliptic Problems (slides or article).
  • Lecture 9 (30.06.2017): Coercivity Lower Bounds (slides: color or article).
  • Lecture 10 (07.07.2017): slides/notes of Lecture 9
  • Lecture 11 (14.07.2017): Linear Parabolic Problems (slides or article).
  • Lecture 12 (21.07.2017): slides/notes of Lecture 11
  • Lecture 13 (28.07.2017): slides/notes of Lecture 111. Linear Parabolic Problems, additional slides/notes on nonsymmetric parabolic problems (slides or article).

Assignments