# Case Studies Scientific Computing (MA4306)

## 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. |

## News

- The application process has started.
- There will be a kick off meeting for all participants in the first lecture week.

The exact date will be published on this website. - In the first weeks after the kick off meeting, there will be some lectures on

some background knowledge for the two projects.

## 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:- Poster presentation
- A short report about 10 to 15 pages summarizing the basic findings of the project
- Well-documented program code that has been developed during the project work
- Plan of milestones and workpackages as well as a time sheet
- Final presentation (15 minutes talk per candidate plus 5 minutes questions per candidate)

## 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:

- last name, first name, student ID
- curriculum (of your master's studies)
- ranking of the projects (which do you find most interesting, which would be a good alternative etc.); please rank all projects. (Example: (1) Project 3, (2) Project 1, (2) Project 4, (3) Project 2 - note that you can rate multiple projects with the same value)
- list of scientific computing related lectures (numerics, numerical engineering, computer science and engineering, etc.) that you have attended (for lectures from other faculties or universities. Please provide the grades you obtained in context of these lectures and give a short description of the topics covered so that we know about your expertise in the field)
- programming skills (programming languages and other programming related skills)
- persons you would like to work with as a team

**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:- Derivation of a heart model based on algebraic equations and ordinary differential equations, i.e. a three-dimensional description of the heart is avoided.

This has the advantage that the simulation times can be remarkably reduced. At this point existing literature can be taken into consideration (see references below). - Selection of suitable numerical solution methods for the mathematical model.
- Development of a GUI (Graphical User Interface) e.g. with MATLAB, which allows the variation of different model parameters. At the same time the influence

of these variations on the ventricular pressures and the blood volume in the ventricles shall be shown. By the help of this GUI one could, for example, determine how a therapy (e.g. pysical-exercise therapy) affects rehabilitation patients with a heart disease by determining the influence of a certain therapy on the model parameters. The new values arising in context of a therapy could then be used as new input parameters for the GUI, so that pressure and volume curves for the improved state could be simulated. By this, differences to the curves corresponding to the unhealthy state could be studied. - The project is to be presented on a website of the HLRS (High Performance Computing Center Stuttgart)
^{}dealing with biomechanical problems. This website contains information about a project that aims to efficiently simulate health-related processes and principles of the human body. Furthermore a cooperation with the platform Imaginary (Digital exhibition, Oberwolfach meets Imaginary)^{}could be considered.

**Contacts:**

- Jürgen Mennel (Marathon runner)
^{} - HLRS (High Performance Computing Center Stuttgart)
^{} - Imaginary (Digital exhibition, Oberwolfach meets Imaginary)
^{}

**References:**

- L. Formaggia, A. Quarteroni and A. Veneziani, eds. Cardiovascular Mathematics: Modeling and simulation of the circulatory system. Vol. 1. Springer Science & Business Media, 2010, Chapter 10.2.
- D. Ambrosi, A. Quarteroni and G. Rozza, eds. Modeling of physiological flows. Vol. 5. Springer Science & Business Media, 2012, Chapter 9.4.
- F. Liang et al. Multi-scale modeling of the human cardiovascular system with applications to aortic valvular and arterial stenoses. Medical & biological engineering & computing 47.7 (2009): 743-755.

### 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^{}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:

- Formulate an optimisation problem with suitable constraints for this problem. Use as a basis the model developed by Vitesco Technology.
- Choose suitable numerical methods to solve this optimisation problem.
- Discuss your simulation results and check whether they are meaningfull.

**Contact:**MSc. Michael Wutz (Vitesco Technology

^{})