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Thesis topics
Bachelor thesis, Master thesis, Projectseminar
Magnetocaloric refrigeration is a promising alternative to conventional vapor-compression cooling technology. The company MAGNOTHERM develops such systems based on high-performance permanent magnets. Recently, recycled magnets, for example from decommissioned MRI systems, have become available as a more sustainable alternative to newly manufactured magnets. However, these recycled magnets exhibit altered and uncertain material properties, such as reduced remanence and increased variability in magnetic characteristics. Understanding how these uncertainties affect the performance and robustness of magnetocaloric devices is essential for assessing the feasibility of recycled materials in industrial applications.
Supervisors: Boian Balouchev, M.Sc. , Prof. Dr. rer. nat. Sebastian Schöps
Bachelor thesis, Master thesis
Conducting numerical simulations to evaluate performance characteristics is an integral part of the electric machine design workflow. Traditionally, these simulations are conducted using the Finite Element Method (FEM), which operates on the mesh — a discrete representation of the underlying design geometry that consists of piecewise-polynomial elements. Curved geometries, e.g. the circular airgap between stator and rotor in an electric machine, are usually represented by Non-uniform rational B-Splines (NURBS) and can not be represented exactly, but only approximated by these finite elements. The NURBS-enhanced Finite Element Method (NEFEM) is a recently proposed extension, in which select elements are modified to allow exact representation of NURBS-curved geometries. The goal of this thesis project is to investigate the applicability of NEFEM to electric machine simulations using an experimental implementation based on the Finite Element solver GetDP. Tasks will include geometric modelling and simulation setup for electric machines and interpretation of results.
Supervisors: Robert Hahn, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps
Bachelor thesis, Master thesis
Integral equation methods are widely used in computational electromagnetics to model open-domain problems such as electrostatic, magnetostatic, or magnetoquasistatic fields. After discretization with basis functions, the resulting linear systems are typically dense, leading to quadratic memory consumption and computational cost.
Hierarchical compression techniques exploit the fact that interactions between well-separated regions of the domain are often of low numerical rank. By approximating these interactions with low-rank representations, both memory usage and computational complexity can be significantly reduced. One such approach is recursive skeletonization, implemented in the MATLAB library FLAM (Fast Linear Algebra in MATLAB).
The goal of this thesis is to investigate the use of FLAM to compress system matrices arising from integral equation formulations. A simple electromagnetic model problem will be discretized and solved both with and without compression. The student will analyze the influence of hierarchical compression on solution accuracy, memory consumption, and computation time. If time permits, the impact of higher-order basis functions on compression efficiency may also be explored.
Supervisors: Merle Backmeyer, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps
Bachelor thesis, Master thesis
Systems with port-Hamiltonian (pH) structure have several beneficial properties, such as power balance and passivity. Moreover, the interconnection of pH systems results in a system that preserves the pH structure. Recently, an energy-based pH framework for field/circuit coupled systems has been proposed. The framework enables the pH structure to be proven for systems containing both field models and circuits, for example in the three-phase transformers. The goal of this project is to show the effectiveness of the proposed framework for systems containing foil conductors. This necessitates implementing a structure-preserving interconnection for the foil conductor model.
Supervisors: Elias Paakkunainen, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps
Bachelor thesis, Master thesis
TRBDF2 (Trapezoidal Rule with Backward Differentiation Formula 2) is one of the standard time integration schemes for circuit simulation. The goal of the thesis is to implement the method, while conforming to the interface specified by the scipy.integrate package. Depending on progress, more recent extensions regarding adaptive time stepping from may also be investigated and implemented.
Supervisors: Peter Förster, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps
Master thesis
Real ferromagnetic materials exhibit complex hysteresis effects, which require memory dependent constitutive mapping between the magnetic field H and the flux density B for solving low-frequency Maxwell’s equations. Operator-based phenomenological approaches, such as the Prandtl-Ishlinskii (PI) model, are widely used for this purpose. In these models, the constitutive relation is typically expressed through a vector-valued, rate independent operator H = V[B]. To effectively integrate such models within a Finite Element (FE) framework, it is necessary to identify beforehand the model's parameters for a given material, such that the model's response provides a better fit to the hysteretic measurements. The aim of this thesis is to investigate and develop a new parametrization procedure, particularly for the generalized stop-type PI models, that improves the accuracy and fittings of the minor and major hysteresis loops. This parametrization, based on the generalized stop-type PI models is carried out for the existing nonlinear stop-type and a newly formulated linear stop-type cases. Initial focus could be given to the parametrization of isotropic materials and further extension to 2d/3d anisotropic cases.
Supervisor: Prof. Dr. rer. nat. Sebastian Schöps
Master thesis
In computational electromagnetics, simulations often need to be evaluated repeatedly for different parameters. Performing full numerical simulations for each parameter configuration can be computationally expensive.
Recent works have explored the use of machine learning techniques, such as deep neural networks (DNNs), Gaussian processes (GPs) and Polynomial Chaos Expansion (PCE), to learn parametric solutions of electromagnetic problems. These approaches enable fast predictions once a model has been trained. In particular they learn the solution in terms of coefficients with respect to a (possibly reduced) finite element or isogeometric basis.
In this thesis, regression-based PCE will be explored as an alternative approach for gradient-enhanced learning. This framework represents the parametric dependence of the solution in terms of a series expansion in orthogonal polynomials.
The thesis will involve a literature review on PCE and the implementation of a PCE-based surrogate model for parametric electromagnetic problems. If time permits, residual-based error estimators or predictive uncertainty intervals for the surrogate model can also be explored.
Supervisors: Merle Backmeyer, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps
Bachelor thesis, Master thesis
The thesis aims to explore non-overlapping domain decomposition methods with optimized transmission conditions for high-frequency Helmholtz problems. Students should first derive the Helmholtz formulation and test methods on a simpler model problem. Successful approaches transition to Helmholtz for a prototype proof-of-concept solver in C++ or Python using an FEM library. Model problem experiments analyze convergence behavior; Helmholtz experiments focus on proof-of-concept if performed. Optional: modelling of application examples and/or numerical algorithm analysis.
Supervisors: Timon Seibel, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps
Bachelor thesis, Master thesis
Most finite element methods can be related to some kind of mesh. In computational electromagnetism, the gradient can be associated with vertices and edges of the mesh. We can exploit this knowledge in simulations by identifying and using a spanning tree, i.e., a selection of #vertices−1 edges that connect all vertices. The vertices and edges are implicitly linked to the topology of the mesh. This can impact simulation as well because a tree might not provide enough information, which necessitates adding additional edges to obtain a belted tree. For the tree construction, the well-known Kruskal’s algorithm is a flexible and simple choice. It requires weights that are assigned to each edge and builds a minimal spanning tree, i.e., it tries to minimize the weights of the edges in the tree. This allows us to control the structure of the tree via specifying appropriate weights.
Supervisors: Devin Balian , M.Sc., Prof. Dr. rer. nat. Sebastian Schöps
Bachelor thesis, Master thesis
This project investigates the validity of equivalent circuit models for the transient analysis of superconducting magnets. Superconducting magnets exhibit complex magneto-thermal behavior during dynamic events such as quenches and current ramps. The study compares simplified equivalent circuit approaches with detailed multiphysics simulations to evaluate their accuracy and limitations. Key performance metrics include voltage evolution, and thermal response during transients. The results aim to assess whether equivalent circuit models provide a reliable and computationally efficient alternative.
In particular, reduced-order circuit representations will be implemented in Xyce. They are benchmarked against existing high-fidelity finite element models developed within CERN’s Finite Element Quench Simulator (FiQuS). While Xyce enables efficient transient simulations based on lumped parameter networks, FiQuS resolves the coupled electromagnetic and thermal fields in two- or three-dimensional space. By systematically comparing both approaches under representative operating scenarios, the project quantifies the trade-offs between computational cost, modeling complexity, and predictive accuracy.
Supervisor: Prof. Dr. rer. nat. Sebastian Schöps
Master thesis
Please note that this is not about the application of FEM with commercial tools, but about developing algorithms to solve BEM/FEM problems, with a strong focus on mathematics.
You develop and implement solution algorithms and programs to simulate eddy current problems based on the Boundary Element Method (BEM) and FEM in C++ (BETL2 framework) and Python. Furthermore, you extend existing simulation software with new features (e.g. coupling multiple BEM domains, impedance boundary conditions). You validate the functionality of the software in applications for position sensors. Last but not least, you evaluate the use of AI methods for mesh optimization.
Details
Supervisor: Prof. Dr. rer. nat. Sebastian Schöps
Master thesis
As an external thesis project, you will explore the world of magnetic position sensors and develop an innovative design of experiments (DOE) approach based on the powerful UQpy library. You will work on mathematical modelling of key parameters as a function of input parameters. One of your tasks will be to connect the developed methods to an electromagnetic finite element simulation (FEM) using Python. You will also have the opportunity to gain deeper insights into the development of models based on artificial intelligence for modelling sensor behaviour.
Details
Supervisor: Prof. Dr. rer. nat. Sebastian Schöps
Bachelor thesis, Master thesis, Projectseminar
When dealing with complex engineering systems, obtaining many field solutions in multi-query scenarios such as design optimization, uncertainty quantification or coupled simulations can become prohibitively expensive. A possible remedy for this problem are so-called surrogate models, which provide a less accurate but computationally cheaper approximation of the field solution. One common type of surrogate model are Gaussian processes (GPs), which often possess advantages in terms of training cost and quality of approximation compared to standard neural network approaches. In previous work, we developed an approach for constructing GP surrogates of parameter dependent stiff ODE solutions using reparameterizations. The aim of this thesis is to extend that approach to the 2D case, illustrating its flexibility and enabling a larger range of applications.
Supervisors: Peter Förster, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps
Bachelor 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: Dr.-Ing. Melina Merkel, Prof. Dr. rer. nat. Sebastian Schöps
