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Case Studies Scientific Computing (MA4306)

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Fig. 1 - Computation of an angle of attack at the tip of a five hohle probe by means of two calibration parameters. Such probes for the determination of angles of attack and velocities can be found e.g. at the front part of airplanes. This problem was part of Project 2: Calibration of multi-hohle probes in the winter term 2019/20.

Organisation

Lecture Prof. Dr. Callies
Question time by arrangement (Email)
Supervision Dr. Tobias Köppl
Requirements Basic courses on numerical mathematics:
MA1304 Introduction to Numerical Linear Algebra
MA2304 Numerical Methods for Ordinary Differential Equations
MA3303 Numerical Methods for Partial Differential Equations
Credits 6 ECTS
TUMonline Link zum TUMonline Eintrag
Moodle To get access to the Moodle course, please register in TUMonline for the lecture. Afterwards you are automatically registered for the Moodle course.

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Basic Concept

Students participating in this module will work on a practical problem in small groups under the supervision of the lecturers (see Fig. 1). The project work typically starts with the discussion of the problem setup, an analysis of the important problem characteristics and a subsequent formulation as a mathematical model. During this phase, the students also present their challenges to a non-scientific audience, usually in the form of a poster presentation. They discuss their poster ideas with the supervisors and receive peer-feedback on their presentations. The participants then research suitable solution algorithms and receive lectures on additional skills where necessary. They discuss their solution approaches with the project supervisors and refine and implement the chosen algorithms. They assess and discuss their solutions and the practical properties of their algorithm with the supervisors and implement necessary modifications or enhancements and / or contrast the properties of different solution approaches with respect to the underlying application. During the project work the students discuss their progress with their supervisors from mathematics and from the field of application on a regular basis and give intermediate presentations of their problem, its characteristics and their solution approaches to the other participants. At the end, the results are presented in the form of conference talks to a scientific audience.

Grading

The final grade is composed of the following subtasks:

Registration

Registration for this course is mandatory and has to be done before the deadline: 1st November 2020.
The registration is done by email to koeppl@ma.tum.de providing the following information:

Please note that there is only a limited number of places for this module, since for each project we can only accept up to three students.

Projects

Project 1: Dimensional reduced modelling of the heart

The heart is located at the center of the human cardiovascular systems, pumping oxygen-rich blood into the vascular network. The oxygen-rich blood flows through blood vessels to the organs, from which oxygen-poor blood is transported back to the heart. In order to enrich the oxygen-poor and carbon dioxide-enriched blood with oxygen again and to lower the concentration of carbon dioxide, the heart pumps the blood back to the lungs. There, blood is again enriched with oxygen from respiration.

From these observations it can be concluded that the heart is an important organ for the human organism. For this reason, the structure and function of the heart is the subject of a large number of publications from the most diverse fields of science, such as sports medicine. In this project work, a simulator is to be developed in cooperation with the High Performance Computing Center in Stuttgart and the marathon runner Jürgen Mennel. This simulator should be used to study the effects of different parameters on the cardiac output. Examples of such parameters are the duration of the heartbeat (pulse) or the elasticity of the heart. The subtasks of this project are as follows:

Contacts:

References:

Project 2: Modelling of a traffic light assistant

Driver assistance systems play a central role in the development of modern cars. Such systems support the driver e.g. in finding optimal routes in consideration of speed limits. In this project, a computational model is to be developed together with the company Vitesco Technology Pfeil that steers a car optimally through the red phases of traffic lights on a given route (see Fig. 2). In this context, an optimal route is characterized by the fact that the driver does not have to brake and accelerate unnecessarily. The subtasks of this project are as follows:

Contact: MSc. Michael Wutz (Vitesco Technology Pfeil)

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Fig. 2 - Space-time trajectories for a route with two traffic lights.

-- TobiasKoeppl - 17 Sep 2020