Dynamical Systems & Scientific Computing - Summer12
Ernst Otto Fischer-Lehrpreis 2012
This course has recently been developed within the Ernst Otto Fischer prize for lecturing of the TUM
- Term
- Summer 12
- Lecturer
- Dr. rer. nat. Tobias Neckel, Dr. rer. nat. Florian Rupp
- Time and Place
- Kick-off meeting: 31.01.2012, 17:00, room 02.07.023
- Audience
- CSE, Mathematics (Master/Diplom), Informatics (Master/Diplom); Modul t.b.a. ; TUMonline details
- Tutorials
- t.b.a.
- Exam
- t.b.a.
- Semesterwochenstunden / ECTS Credits
- 6 SWS / 9 Credits
- TUMonline
- {{{tumonline}}}
Survey
"Dynamical Systems & Scientific Computing" introduces the theory and numerics of randomly disturbed differential equations from the point of view of both Dynamical Systems and Scientific Computing. This newly introduced course is designed as a seminar with a dedicated workshop part supplemented by exercises and some few lectures. The course is open (and meant for) students of mathematics as well as informatics: This interesting combination of different backgrounds will allow for fruitful discussion and solution approaches.
The focus of this course is on the student-centred approach to the topics during the seminary part. In the 3-day workshop, the participants apply their kowledge to a specific problem on earthquake responses in multi-storey buildings. Most parts of the so-called simulation pipeline are, thus, tackled in a hands-on approach:
- Theory
- Modelling
- Numerics & Algorithms
- Implementation & Data Structures
- Visualisation
- Verification & Validation
The major innovative element of this course is the workshop: The task is to realise a small software product in matlab. The participants will experience (parts of) the challenges and requirements of interdisciplinary projects in academia and industry.
Content
The seminary talks are chosen from the following topics. Details will be discussed during the kick-off meeting on January 31, 2012, at 17:00 in room 02.07.023.
Topics
Dynamical Systems & Randomly Perturbed Differential Equations
- Classical theory of ordinary differential equations (ODE) and corresponding numerics
- Dynamical systems and stability of equilibria
- Solution concepts of random differential equations
- Numerics of random differential equations
- Stochastic stability
Algorithms of Scientific Computing
- Reduction or partial differential equations (PDE) to systems of ODE using spatial discretisation
- Basic numerical methods for (deterministic) ODE
- Fourier transform
- Discrete Sine transform
- Space-filling curves
Application: Modelling seismic activities for buildings
- Modelling the dynamics of elastic bodies
- Relevant aspects of Software Engineering
- Visualisation techniques