Stochastische Finite Elemente Methode

BGU60019Master's Modules6 ECTSEnglishwinter semesterLehrstuhl für Risikoanalyse und Zuverlässigkeit (Prof.Straub)

AI-edited module sheet. Based on the TUMonline module description, edited for readability.Original in TUMonline

What it is about

You will learn the fundamentals and numerical methods of stochastic finite element method for uncertainty quantification in elastostatic systems. In the end you will be able to describe random variables and random fields, discretize random fields, and apply both Monte Carlo and spectral methods for uncertainty propagation in linear elastostatic problems.

What you will be able to do

Understand the basic concepts of probability theory
Define Random Vectors and Random Fields by their second moments
Discretize random fields into a finite number of random variables
Assess the suitability of different stochastic discretization methods
Apply Monte Carlo methods for uncertain finite element systems
Apply spectral stochastic finite element methods

What the module consists of

VorlesungConveying theoretical concepts and methods; weekly sessions
ÜbungsaufgabenDeepening of the methods; partly with software requirements (Matlab/Python)

Teaching method

Tafelunterrichtfor the step-by-step derivation of theoretical concepts and mathematical formulations
Präsentationen/Slidesfor graphical illustration and clear presentation of complex content
Hausaufgaben mit Musterlösungento consolidate the material; selected problems are discussed in the lecture
Software-gestützte Übungen (Matlab/Python)Application and implementation of the methods

What you should already know

Lineare Finite-Elemente-Methode (1D lineare Elastizität)
Grundkenntnisse der Wahrscheinlichkeitstheorierecommended
Grundkenntnisse in Matlabrecommended

Assessment

Written examOpen-Book

Open-book written examination, 90 minutes. You should demonstrate that you master the concepts, methods and tools of the course, build probabilistic models for uncertain inputs, and apply stochastic finite element methods for uncertainty propagation in linear elastostatic problems.

Exam date10.03. · 14:00–15:302750, Karl Max von Bauernfeind Hörsaal (0507.03.750)

Reading list

Kleiber, M.; Hien, T.D. - The stochastic finite element method. Basic perturbation and computer implementation.
Ghanem, R.G.; Spanos, P.D. - Stochastic finite elements: A spectral approach.
Sudret, B.; Der Kiureghian, A. - Stochastic finite elements and reliability: A state-of-the-art report.
Xiu, D. - Numerical methods for stochastic computations: A spectral method approach.
Cliffe, K.A.; Giles, M.B.; Scheichl, R.; Teckentrup, A.L. - Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients.

Dates

LectureStochastic Finite Element Methods2 groups to choose from

AFri09:45–11:15
2601, Übungsraum (0506.02.601)
15× · 16.10.–05.02.
- 16.10.
- 23.10.
- 30.10.
- 06.11.
- 13.11.
- 20.11.
- 27.11.
- 04.12.
- 11.12.
- 18.12.
- 08.01.
- 15.01.
- 22.01.
- 29.01.
- 05.02.
BMon08:45–11:15
N3823, Seminarraum (0108.03.823)
15× · 12.10.–01.02.
- 12.10.
- 19.10.
- 26.10.
- 02.11.
- 09.11.
- 16.11.
- 23.11.
- 30.11.
- 07.12.
- 14.12.
- 21.12.
- 11.01.
- 18.01.
- 25.01.
- 01.02.

From the current semester, not binding. You attend one of several groups; the timetable automatically suggests the one with the fewest clashes.

Show TUMonline data

Sprache: Englisch
Turnus: Wintersemester
Modulniveau: Master
Moduldauer: Einsemestrig
Gesamtstunden: 180
Präsenzstunden: 75
Eigenstudiumstunden: 105
Organisationsname: Lehrstuhl für Risikoanalyse und Zuverlässigkeit (Prof.Straub)

Courses

Stochastische Finite Elemente Methode

Official page in TUMonline · Details are not binding.