Nowadays, the use of lighter structures demands for the consideration of elastic effects for many components. Mostly, the modeling and numerical simulation of elastic bodies is achieved with the ï¬nite element method, which often leads to a high number of degrees of freedom, more than a million degrees of freedom is not unusual. Therefore, one essential step for an efficient simulation is the reduction of the elastic degrees of freedom. The complex model is replaced with a far simpler one, which still accurately captures the most important aspects of the phenomena being modeled.
This course presents the basic mathematical theory for projection-based model reduction. The lecture is accompanied by exercises, mainly practical Matlab programming exercises.

Course Outline:

Introduction / mathematical basics for model reduction / error analysis / modal reduction techniques / basics from control theory / reduction of second order MIMO systems / Krylov-based model reduction / methods based on Gramian matrices / Proper Orthogonal Decomposition / numerical methods used for model reduction / model reduction of large scale systems (excursion to the HLRS) / SVDMOR / nonlinear model reduction of mechanical systems / current research topics in model reduction of mechanical systems (parametric approaches)

Lecture Information

Audience:
The lecture is intended for students in their Msc programme as well as SimTech students.

Extent: 3 credit points (2 SWS)

Lecture:

Tuesday, 8:00 a.m. to 9:30 a.m., V7.04

The lectures begins on Tuesday, April 18th, 2017

Excercises: The lecture is accompanied by exercises, mainly practical Matlab programming exercises. It is allowed to work on them in groups of 2 to 3 students. Please upload only one solution per group to ILIAS.

Exam: A written exam is planned but depending on the amount of participants it could be substituted in favor of an oral exam.