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Case Studies Scientific Computing (MA4306)

Modern numerical methods (e.g. methods for solving ordinary and partial differential equations, methods for the iterative solution of large linear systems and inverse problems, approximation methods for scattered date, uncertainty quantification ...) are applied to application problems. These problems are obtained from other faculties, from external research institutes or from industry. The complete solution chain has to be carried out (modelling, analysis, solution, presentation).

NSZylinderFlow.png

Turbulent flow pattern around a cylinder obtained from solving the Navier-Stokes equations.

Lecture Prof. Dr. Rainer Callies, Dr. Tobias Köppl, Monday 12:15 - 13:45 in MI 02.08.011 and individual lectures (see timetable)
Question time by arrangement (Email)
Supervision Prof. Dr. Rainer Callies
Dr. Tobias Köppl
Fabian Wagner
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 7 ETCS
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. 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:

Projects

Project 1 & 2: Simulation-based uncertainty quantification in 1D blood flow models (Dr. Köppl, Wagner)

Blood flow in human arteries depends on several parameters like cross section area and wall thicknesses. For a simulation of flow rate and pressure curves one can use Navier-Stokes equations and elastic or viscoelastic equations which are coupled together and simplified to a one-dimensional hyperbolic PDE-system. In order to get an understanding how flow and pressure change while parameters vary, parameters are modelled as random variables governed by a certain probability distribution. Generating random samples of the underlying distributions and solving the PDE-system with respect to each sample, one can analyse statistically how the parameters influence the quantities of interest. This is a typical task in forward uncertainty quantification (UQ).
Conversely in inverse UQ, the flow and pressure are given by measurements and the parameters which recover the data are unknown. The inverse problem could be solved by applying Sequential Monte Carlo in order to shift the prior distribution of the parameters into a posterior distribution that recovers the true unknown parameter.

The two projects are divided as follows:

Project 3: Simulation of heat transfer in a concentrated solar powerplant (Dr. Köppl)

The use of solar energy plays a major role in the generation of renewable and sustainable energy. One way of harnessing solar energy is to build concentrated solar powerplants. Thereby, mirrors or lenses are used to concentrate a large area of sunlight, onto a small tube located in the focal point of the mirrors or lenses. The tube is filled with a fluid consisting mostly of saltwater. At the inlet the fluid enters with a low temperature which is heated as long as the tube is irradiated. After heating the fluid, the stored thermal energy can be used to produce electricity or it can be directly used for the production of chemical products. The propagation of heat within the tube is governed by the heat transfer equation. The components of this equation are a time derivative, a convective term governed by the fluid velocity, a diffusive term as well as a possible source term.

The milestones of this project are as follows:

Project 4: Bayesian inversion and sensor design for biological imaging (Prof. Dr. Ullmann, Dr. Jüstel, Wagner)

Optoacoustic or photoacoustic tomography (PAT) is a hybrid imaging technology that produces images of biological tissue with optical contrast and acoustic resolution. Near infrared laser pulses are used to illuminate the tissue. The subsequent energy absorption and conversion to heat produces an acoustic pressure variation which travels through the object and can be recorded by ultrasound transducers. PAT has many biomedical applications, e.g. the detection of tumors or the reconstruction of blood oxygenation of tissue in vivo. Mathematically, PAT is a difficult nonlinear and ill-posed inverse problem where acoustic and optical inversion are coupled. In this project we focus on the initial step, namely the acoustic inversion. The goal is to infer the initial pressure distribution given the pressure measurements recorded on the surface of the object. The initial and final pressure are linked by the linear acoustic wave equation. Moreover, we employ a Bayesian approach by assuming a certain prior distribution for the initial pressure. This is combined with the measurements to give a posterior distribution.

The milestones of this project are:

Project 5: Simulation of a wind energy turbine (Prof. Dr. Callies)

Registration

Registration for this course is mandatory and has to be done before the deadline: 3rd April 2019.
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 three to four students. The application process for this module starts after the preliminary meeting.

Preliminary Meeting

The first meeting takes place on 26th March 2019 from 10:15 am to 11:45 am in room MI 00.07.014.
The topics of this meeting are

-- FabianWagner - 11 Mar 2019