Directly to

 

MOR lecture (winter 2017/18)


Scope

The aim of the lecture is to provide an introduction to different model order reduction techniques mainly designed for linear problems with parameter dependency. Discrete mechanical systems (springs/trusses) are treated in quasi-static and dynamic settings. Substructuring techniques such as static condensation are covered. Further, reduced basis methods using Galerkin projections are proposed. Different techniques for the generation of the reduced basis are proposed. Uncertain material parameters in large scale spring systems are used to demonstrate the capabilities of the proposed techniques.

Continuum mechanical problems are investigated in terms of the stationary and instationary heat equation and quasi-static linear elastic problems. For the continuous problem settings the use of a reduced basis in combination with Galerkin projections is investigated. Sampling techniques for an improced numerical efficiency are outlined. The snapshot proper orthogonal decomposition is proposed in order to compute the reduced basis from preliminary offline computations.

The course is accompanied by a computer lab (programming language MATLAB). The participation in the computer lab is obligatory in order to be egligible for the oral examination at the end of the course. The material for the computer lab will be provided on this site.

[back to top]


General course information

The lecture will be held in Pfaffenwaldring 9, lecture hall V9.31 on Monday, 11:30-13:00h. The accompanying computer lab will be held in the COMMAS computer pool (Pfaffenwaldring 7, first floor, V7.12). The date and time for the computer lab will be announced within the first week. Students can work in the COMMAS computer pool 5 Minutes from prior to 5 Minutes after the computer lab. A timetable for the computer lab will be available on ILIAS. Office hours will be offered during the lecturing period (to be precised during the course).

Lecture Notes will be provided in printed form for a small fee.

PDF announcement

[back to top]


Material (lecture and computer lab)

Registration via CAMPUS is required. This implies the membership in ILIAS. The material for the course is exclusively available for registered members in ILIAS

[back to top]


Literature

Introductory text books are, e.g. (references are also available via ILIAS)

A. Quarteroni, A. Manzoni, F. Negri Reduced Basis Methods for Partial Differential Equations in: UNITEXT - La Matematica per il 3+2, Vol. 92, Springer Switzerland, 2016

F. Chinesta, P. Ladevèze Separated Representations and PGD-Based Model Reduction: Fundamentals and Applications in: CISM International Centre for Mechanical Sciences, Courses and Lectures, Vol. 554, Springer, 2014

A. T. Patera, G. Rozza Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations Version 1.0, Copyright MIT 2006-2007, to appear in (tentative rubric) MIT Pappalardo Graduate Monographs in Mechanical Engineering; WWW (available online)

[back to top]