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Reduced Basis Methods - Single View

Basic Information
Type of Course Lecture Long text
Number 106363 Short text
Term WiSe 2021/22 Hours per week in term 4
Expected no. of participants Study Year
Max. participants
Credits Assignment enrollment
Hyperlink
Language english
Dates/Times/Location Group: [no name] iCalendar export for Outlook
  Day Time Frequency Duration Room Room-
plan
Lecturer Status Remarks Cancelled on Max. participants
iCalendar export for Outlook Tue. 08:00 to 10:00 weekly to 25.01.2022  Einsteinstr. 64 - M B 6 (M 6)        
iCalendar export for Outlook Fri. 08:00 to 10:00 weekly to 28.01.2022  Einsteinstr. 64 - M B 6 (M 6)        
Group [no name]:
 


Responsible Instructor
Responsible Instructor Responsibilities
Rave, Stephan, Dr. responsible
Curriculae
Graduation - Curricula Sem ECTS Bereich Teilgebiet
Master - Mathematik (88 105 13) -
Master - Mathematik (88 105 10) -
Master - Mathematics (88 F23 20) -
Exams / Modules
Number of Exam Module
22001 Vorlesung mit Übungen - Master Mathematik Version 2013
18004 Vorlesung 2 (mit Studienleistung) - Master Mathematik Version 2013
18003 Vorlesung 2 (ohne Studienleistung) - Master Mathematik Version 2013
12001 Lecture - Master Mathematics Version 2020
20003 Lecture 2 - Master Mathematics Version 2020
Assign to Departments
Fachbereich 10 Mathematik und Informatik
Contents
Description

Many physical, chemical or biological processes can be described with the help of partial differential equations. Since an analytical solution of the equations is rarely possible, numerical discretization methods must be applied in order to be able to analyze and predict the behavior of these processes. However, despite the many technical advances in high-performance computing, for many applications even a numerical solution can only be obtained with considerable effort. It is therefore of great interest to develop model reduction methods which, starting from a given high-dimensional discrete model can provide efficient surrogate models of low dimension that deliver fast and accurate predictions for varying model parameters.

In this lecture we will primarily consider so-called reduced basis methods for parameterized partial differential equations. These methods are based on a (Petrov-)Galerkin projection of the solution onto a suitably chosen low-dimensional subspace of the discrete solution space. The resulting reduced order models can then be studied using well-known techniques from numerics of partial differential equations (Céa lemma, residual-based error estimators, etc.). Using results from approximation theory, appropriate algorithms for constructing the reduced solution space can be devised that guarantee the quality of the resulting reduced order model. In the integrated practical exercises of this course, we will gain hands-on experience with the application of reduced-basis methods to concrete examples using the model-reduction library pyMOR.

Remarks

The course will start on Tuesday, October 19.

Prerequisites

Knowledge of the finite-element method is helpful but not strictly required. For the practical exercises, basic knowledge of the Python programming language is expected.


Structure Tree
Lecture not found in this Term. Lecture is in Term WiSe 2021/22 , Currentterm: WiSe 2022/23