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### Thesis topics

Bachelor thesis, Master thesis, Projectseminar

High-temperature superconducting (HTS) materials are a promising technology for high-field magnets in particle accelerators. In particular, no-insulation (NI) coils, i.e., coils wound without turn-to-turn insulation, have gained popularity due to their robustness [1]. Numerical methods such as the finite element (FE) method play a key role in developing HTS-based applications. The objective of this project is to extend CERN’s existing open-source Finite Element Quench Simulation (FiQuS) framework with 2D axisymmetric FE models of NI coils [2]. Since they are more efficient but less general than existing 3D models, they will complement the latter as an important tool in FiQuS to analyze NI coils. Following FiQuS’s ideals, a key aspect will be to hide the complexities CERN of the FE formulation from the users who are typically not FE experts.

**Supervisors**: Erik Schnaubelt, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsBachelor thesis, Master thesis, Projectseminar

CERN started a project last year to build a comprehensive open-source quench simulation tool called FiQuS (Finite Element Quench Simulation). It is based on the finite element (FE) framework ONELAB and written mostly in Python. The idea is to build a flexible tool which allows users to build and simulate complex models from human-readable inputs hiding the complexity of the FE kernel. In order to simulate real-world accelerator magnet circuits, this project aims at coupling FE magnet models from FiQuS with electric circuits [1], which can then be solved by circuit simulators such as Xyce. A key aspect will be to hide the complexities of this coupling from the users who are typically not FE experts.

**Supervisors**: Erik Schnaubelt, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsMaster thesis

Solving partial differential equations numerically with boundary element methods requires the application of fast methods to be competitive with other numerical methods. At high-frequencies, the existing implementation of H2-matrices breaks down and needs to be adapted in order to work efficiently.

The idea of the approach is to approximate a spherical wave in far distance hierarchically by plane waves. The implementation is carried out in the C++ library Bembel, see . www.bembel.eu

**Supervisors**: Maximilian Nolte, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsBachelor thesis, Master thesis, Projectseminar

Electric energy conversion is a key issue on the way to decarbonization. Computational design and optimization of electric motors is a very active research area with the aim to increase the efficiency and power density of electric drives. Yet, optimization in commercial solvers is often performed using time-consuming methods such as surrogates or genetic algorithms, taking days or weeks for one optimization.

This work combines the modeling of the motor using Isogeometric Analysis (IGA), which allows to exactly represent the geometry, with fast gradient based optimization. By using present state-of-the-art numerical modeling techniques together with efficient optimization algorithms, it is possible to reduce the optimization time to several minutes.

**Supervisors**: Michael Wiesheu, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsBachelor thesis

When assembling the system matrices of the boundary element method, the distance between two objects must be determined in an efficient way. At the moment, a very rudimentary but fast method is used. However, one could also use geometric quantities such as the control points and the knot insertion algorithm from isogeometric analysis, as shown below, to do this more accurately. The implementation is carried out in the C++ library Bembel, see . www.bembel.eu

**Supervisors**: Maximilian Nolte, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsBachelor thesis

The need for higher energy efficiency and decarbonization give rise to a steadily increasing importance of electric drives. Simulations allow the physical limits to be pushed in order to increase the power density and make motors more cost-efficient. This work aims to investigate the influence of mechanical stresses in electric motors on the electromagnetic behavior and find out how stress dependent material properties can be mitigated or exploited. Simulations are performed in an Finite Element (FE) framework using Isogeometric Analysis (IGA), which allows to exactly represent the geometry. This enables an efficient coupling of the geometric, magnetic and mechanical systems.

**Supervisors**: Michael Wiesheu, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsSeminar paper, Bachelor thesis, Proseminar

Parabolic partial differential equations (PDEs) as the eddy current problem or the heat equation depend both on the space and on time. For simulating these problems one often chooses a method of lines approach, i.e., the space is discretized first and the arising system of ordinary differential equations (ODEs) is solved with a time integration scheme. In this context, one can apply domain decomposition approaches and Parallel-in-Time (PinT) methods to increase efficiency through parallelization.

This thesis deals with applying the PinT method ParaReal to the heat equation. For domain decomposition and space discretization a code framework based on mortaring and IsoGeometric Analysis (IGA) is provided. We want to apply the examined methods for the simulation of electrical machines (eddy current problem), so another focus lies on the validation of results and measuring the increase in efficiency in comparison to other approaches.

**Supervisors**: Mario Mally, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsMaster thesis

Parallelizable domain decomposition approaches gain attention due to an increase in parallel computation power. Hence, it is interesting to expand the well-established Finite Element Tearing and Interconnecting (FETI) method by different basis functions and more general coupling settings. Currently, we want to apply a variant based on IsoGeometric Analysis (IGA) and mortaring to efficiently simulate electrical machines in 3D. This thesis contributes to the goal by exploring different approaches to crosspoint modification, solver structures and preconditioning. In this context, we want to differentiate between dual-primal and all-floating methods.

In the all-floating (or total) approach, Dirichlet boundary boundary conditions are enforced weakly in addition to the coupling constraints. One additionally requires coupling modifications to obtain a solvable discrete system. For dual-primal FETI, one enforces the coupling conditions in a strong sense at crosspoints and Dirichlet boundaries. Additionally, boundary conditions are considered in a more usual way.

**Supervisors**: Mario Mally, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsSeminar paper, Bachelor thesis, Proseminar

For accurate and efficient simulations of electrical machines in 3D several prospective approaches are examined in more detail within the . One of which is the application of parallelization through domain decomposition. In order to obtain scalable solvers, preconditioning is a necessity because the number of iterations for reaching a certain tolerance in an iterative solver can be decreased. CRC TRR 361

In this work you are provided with code for generating discrete domain decomposition problems which is based on IsoGeometric Analysis and a mortaring approach. After familiarizing yourself with the theory and the implementation, different preconditioning approaches need to be explored and compared to each other.

**Supervisors**: Mario Mally, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsBachelor thesis

Particle accelerators rely on electromagnets for deflecting and focusing the particle beams. The simulation of the magnetic field, generated by normal conducting accelerator magnets depends among others on material and geometry parameters of the iron yoke. While the forward simulation of the magnetic field given the parameters is well understood, the inverse problem, that means the recalculation of physical meaningful parameters given field measurements, remains challenging. Nevertheless, solving the inverse problem is interesting for reverse engineering as well as for updating parameters in order to improve the simulations.

TU Darmstadt, together with the European Organization for Nuclear Research (CERN) formulated optimization problems that correspond to these inverse prob- lems. The investigation of optimization algorithms suitable for these problems is the goal of this thesis.

**Supervisors**: Luisa Fleig, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsSeminar paper, Bachelor thesis, Master thesis

LEDs are ubiquitous as light sources for a wide variety of use cases. During product development, they have to be tested under different environmental con- ditions. Since standard LED based lighting systems have a lifetime of several thousand hours, this usually does not include extensive lifetime prediction tests. The state-of-the-art are empirical and physical models based on the limited data that is available.

The aim of this thesis is to combine the existing approaches with techniques from machine learning. One particularly interesting method is kriging, as it allows to estimate both the lifetime and its uncertainty based on the measurement data. This enables new ways for adaptive design of experiments (DOE), which may help to streamline and speed up the testing procedures. Lastly, it is of great interest to investigate learning strategies that include hard physical constraints of the underlying process, such as positivity or monotonicity.

**Supervisors**: Peter Förster, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsBachelor thesis, Master thesis

Superconducting magnets as e.g. used in particle colliders such as the LHC at CERN exhibit complex transient magneto-thermal phenomena whose analysis requires appropriate numerical methods such as the finite element (FE) method. When using the latter, thin insulation layers can lead to numerical problems in Contact: thermal simulations due to their high aspect ratios.

To circumvent this problem, thin shell approximations collapsing the volumetric insulation layer into a surface can be used. However, without further considerations, these methods require the meshes on both sides of the shell to be conforming. In order to conveniently treat layer-to-layer insulation of superconducting magnets, a way to deal with non-conforming meshes is desirable.

Mortaring methods are a well-known possibility to cope with non-conforming meshes. Thus, this announcement proposes to implement mortaring for thin shell approximations in the open-source finite element framework GetDP.

**Supervisors**: Erik Schnaubelt, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsMaster thesis

Due to their high sensitivity, magnetoelectric (ME) sensors consisting of multiferroic composite materials have wide application areas, mainly focusing on the medical field, e.g. for measuring biomagnetic signals in the diagnostics of human brain or heart functions. These ME are based on composites with magnetostrictive and piezoelectric layers that are usually accompanied by a layer of substrate, made of e.g. silicon or steel. The modeling and simulation of such ME composite structures is particularly challenging as it involves partial differential equations that couple the electric, magnetic and mechanical fields.

The master thesis aims at extending already existing mathematical models to include the piezoelectric effect and simulating the resulting PDEs with the open-source solver GEOPDEs, which uses Isogeometric Analysis (IGA), a generalization of the Finite Element Method (FEM) based on splines that enables exact geometry description.

**Supervisors**: Dr. rer. nat Mané Harutyunyan , Prof. Dr. rer. nat. Sebastian SchöpsSeminar paper, Bachelor thesis, Master thesis, Projectseminar

Deviations in the manufacturing process of electronic components may lead to rejections due to malfunctioning. Uncertain design parameters (i.e. geometrical and material parameters) can be modeled as random variables. Then, the failure probability of a realization can be estimated. A standard approach for estimating failure probabilities is a Monte Carlo analysis. In a Monte Carlo analysis a large number of sample points is generated according to a given probability distribution. The percentage of sample points not fulfilling some predefined performance feature specifications denotes the failure probability. In order to obtain a reliable estimation, a large number of sample points is required. This leads to high computing costs, since for each sample point a PDE must be solved, e.g. with the finite element method (FEM). Current research deals with the reduction of computational effort. Importance sampling is an approach to reduce the number of FEM evaluations by generating sample points in critical regions with a higher probability.

**Supervisors**: Mona Fuhrländer, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsSeminar paper, Bachelor thesis, Master thesis, Projectseminar

Electron guns represent the first stage of linear accelerators. As such, they have to fulfill a number of criteria: provide a focused beam of high enough energy, abide by space and weight constraints and not interfere with the vacuum conditions of the surrounding chamber. A lot of research has been done to design guns that meet all the above requirements, however these approaches often optimize individual parts separately, unneccesarily constrain the design space or make strong assumptions in order to obtain a more easily solvable problem.

This thesis aims to create a holistic design approach for electron guns that is based on shape optimization using the isogeometric analysis (IGA) package GeoPDEs and the particle tracking code ASTRA. A further point of interest are more advanced optimization techniques (e.g. employing shape derivatives) and increasing the efficiency of the software.

**Supervisors**: Peter Förster, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsBachelor thesis, Master thesis

Due to the growing importance of e-mobility, the efficient simulation and optimization of electric energy converters, in particular electric machines, is becoming increasingly important. In the manufacturing process of these electric machines imperfections and small deviations from the nominal design can occur. In the worst case, these imperfections can lead to a significant decrease in quality or even failure of the machine. To avoid this, the machine can be optimized robustly, i.e., considering the deviations in the machine design. Robust optimization aims to find a machine design which is robust in terms of deviations from the nominal design, i.e., to find an optimum in terms of a goal function

*J*which does not deteriorate significantly for small changes in the design parameters*p*, compare Fig. 2. In this project an electric machine is simulated using isogeometric analysis and the shape of the machine shall be optimized robustly considering uncertainties, using uncertainty quantification methods like the Monte Carlo method.**Supervisors**: Melina Merkel, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps