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### Thesis topics

Bachelor 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 SchöpsHiWi Position

Material relations are a key factor when it comes to accurate simulations of complex machines such as the superconducting magnets of the LHC particle collider at CERN. To this end, a lot of effort is spent on finding appropriate fits of various different materials under various different operating conditions. The results are typically kept in libraries, in the case of CERN as functions written in C (see here). These functions are then to be used in different simulation tools which, however, often require a translation of the material function into a different programming language (typically, to python or Matlab).

So far, this translation is done mostly manually. This implies that changes to the common basis C functions require changes in all translated versions as well. To avoid this cumbersome manual process, this announcement proposes an automatic wrapper generation of the base C function to other programming languages using, for example, the software development tool SWIG.

**Supervisors**: Erik Schnaubelt, M.Sc., Prof. Dr. rer. nat. Sebastian SchöpsHiWi Position

CERN recently started a project to build a comprehensive open-source quench simulation tool called FiQuS (Finite Element Quench Simulation). It is based on the finite element (FE) framework GetDP and FE mesher Gmsh. The idea is to build a flexible tool which allows users to build and simulate complex models from human-readable input files hiding the complexity of the underlying kernel.

FiQuS is written mostly in python with small parts written in GetDP’s own scripting language. Following modern software engineering standards, focus is put on continuous integration and deployment, in particular comprehensive testing of all parts of the software. Furthermore, the use of high-performance computing is planned to be integrated while keeping the tool simple to use.

We are looking for a motivated student to help our team shape FiQuS and make this new and demanding project succeed. The exact details of the work can be discussed depending on the wishes of the student and range from software engineering tasks to building finite element models. Possible duties may include

• Setup of automated and comprehensive testing in the CI/CD pipeline

• Maintenance of the gitlab project including CI/CD, wiki, documentation

• Development of template finite element formulations or model geometries

• Preparation of the tool for use of high-performance computing methods

**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