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Themenvorschläge
Masterarbeit
TU Darmstadt, together with the universities of Basel, Bonn and Lugano, develops the free isogeometric boundary element library Bembel, see www.bembel.eu. The library is well-suited for electromagnetic applications in which highly accurate solutions are required. For such problems, the commonly-used IEEE 754 floating-point standard may arise as a bottleneck to the accuracy of the numerical solution, as rounding errors can become dominant. Thus a more flexible number representation is expected to become advantageous. The purpose of this master thesis is to replace the numerical backend of Bembel, currently implemented in the eigen linear algebra library, with MTL, a numerical backend in which the floating-point standard can be exchanged easily.
The thesis can be supervised by TU Darmstadt, a partner university (e.g. Lugano) or by one of the industrial partners, i.e., SimuNova or Stillwater Supercomputing.
Betreuer/in: Prof. Dr. rer. nat. Sebastian Schöps
Bachelorarbeit, Masterarbeit
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.
Betreuer/innen: Melina Merkel, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps
Bachelorarbeit, Masterarbeit
The company Signify (former Philips Lighting) in Eindhoven is the world leader in lighting products. Their products are designed and optimized by computer aided design workflows including uncertainty quantification (UQ). UQ is a technique for example used to analyze the impact of manufacturing imperfections on the products. Nowadays, companies aim for six sigma processes, i.e. the variation is assumed to be normally distributed and >99% of all outcomes shall be free of defects.
This thesis shall analyze, investigate and implement methods for UQ of power electronic and analog circuitry at Signify. This requires to understand the existing simulation workflow at Signify and the (random) influences that may lead to defects. Based on this understanding UQ methods, e.g. (quasi) Monte Carlo, surrogate-based Monte Carlo or polynomial chaos techniques, can be selected and possibly extended if necessary. Finally, an uncertainty quantification workflow shall be established, e.g. by writing code and user interfaces.
Betreuer/innen: Dr.-Ing. Niklas Georg, Prof. Dr. rer. nat. Sebastian Schöps
Masterarbeit
Within the last four years, a boundary element simulation framework for the solution of electrostatic, acoustic, and electrodynamic problems for 3D applications called BEMBEL has been developed together with the universities of Twente (Netherlands) and Lugano (Switzerland). The project had a signifficant impact in science and industry, due to its efficient use of the concept of isogeometric analysis within a Galerkin framework. However, many applications require the solution of 2D problems, which BEMBEL does not currently support. This thesis aims to close this gap through the implementation of a fully integrated 2D simulation framework for the numerical solution of the Laplace and Helmholtz equation, build upon existing routines and expert knowledge of the cooperation partners in Twente and Lugano.
Betreuer/innen: Dr.-Ing. Felix Wolf, Prof. Dr. rer. nat. Sebastian Schöps
2019
Studienarbeit, Bachelorarbeit, Masterarbeit
The Finite element method (FEM) in the frequency domain is one of the most powerful methods for the solution of high frequency electromagnetic field problems for resonators, filters, attenuators,etc. In many practical applications, however, the frequency response of the system over a broad frequency band is required.Fast Frequency Sweeping (FFS) is a class of methods used for the estimation of broadband S-parameters based on evaluation of a minimum amount of frequency points. Modern FFS methods include Reduced Basis Methods, Thiele based interpolation, Asymptotic Waveform Evaluation and Vector Fitting. Each of the methods have advantages and disadvantages depending on the specific characteristics of the frequency response of the system.
Betreuer/innen: PD Dr. rer. nat. Erion Gjonaj, Prof. Dr. rer. nat. Sebastian Schöps
Studienarbeit, Bachelorarbeit, Masterarbeit
Isogeometric analysis (IGA) is a finite element method (FEM) using splines for geometry description and basis functions such that the geometry can be exactly represented. Recently, an isogeometric mortar coupling [1] for electromagnetic problems was proposed. It is particularly well suited for the eigenfrequency prediction of superconducting accelerator cavities. Each cell, see Fig. 1, can be represented by a different subdomain but may still share the same discretization. The approach leads to a (stable and spectral correct) saddle-point problem. However, its numerical solution is cumbersome and iterative substructuring methods become attractive. The resulting system is available from a Matlab/Octave code. In this project the finite element tearing and interconnect method (FETI) shall be investigated and standard, possibly low-rank,preconditioners implemented and
Betreuer/in: Prof. Dr. rer. nat. Sebastian Schöps
Studienarbeit, Masterarbeit
The focus of this work is the adaptive construction of the polynomial surrogate modelin order to mitigate the curse-of-dimensionality. The efficiency of this approach shall be further improved by employing adjoint-based error measures.
Betreuer/innen: Dr.-Ing. Niklas Georg, Prof. Dr. rer. nat. Sebastian Schöps
