Reduced Basis Methods

This course consists of two 2-hour lectures and one 2-hour exercise per week (4+2 SWS, 9 LP).

News

  • The first lecture will take place on the 24th of April at 10:00 in HeHo 18, room 1.20.
  • The first exercise sheet will be online on the 26th of April.
  • The first exercise will take place on the 3rd of May at 10:00 in HeHo 18, room E60.
  • Exercise sheets will be put online in moodle. Students have to register for the class in moodle, the password will be provided at the beginning of the first lecture (or email the exercise supervisor).

Content

Topics:

  • Parametric PDEs
  • Reduced Basis Approximation
  • Proper Orthogonal Decomposition (POD)
  • A-posteriori Error Analysis
  • Greedy Algorithms
  • Empirical Interpolation Method (EIM)
  • Time-Dependent Problems
  • Space-Time Discretizations
  • Non-Linear Problems

Schedule

LectureWed 10-12HeHo 18, room 1.20
Thu 8-10HeHo 18, room 1.20
ExercisesFri 10-12HeHo 18, room E.60

Exam

To be admitted to the exam you have to actively participate at the exercises and acquire a minimum of 50% of all exercise points.

Exam dates and form tba.

Exercise Sheets

Exercises will take place Fridays, weekly. Exercise sheets will be put online a week before the exercise in moodle. You need to register in moodle for this class, registration password will be provided at the first lecture or write an email to the exercise supervisor.

Exercises will be conducted by a "voting" system. At the beginning of each exercise you have to cross the exercise problems you are ready to present. For each problem a student will be selected at random to present their solution.

If the solution is mostly correct and the student can explain their solution (subject to judgement of the exercise supervisor), the student gets full points for all of the problems they crossed out on the sheet. Otherwise the student forfeits all of their points for that exercise.

You require 50% of all points to be admitted to the exam.

Script

There will be no script for this lecture. Here is a link to old lecture notes from summer 2012, typed by a student.

Literature

A. Quarteroni, A. Manzoni and F. Negri: Reduced Basis Methods for Partial Differential Equations, Springer 2016.

Model Reduction and Approximation: Theory and Algorithms, SIAM 2017. Edited by P. Benner, A. Cohen, M. Ohlberger and K. Willcox.

Lecture

Exercises