Thesis topics

8 items found. Show all theses.

• 2019

  Parareal for Differential-Algebraic Equations with Strangeness

  Seminar paper, Bachelor thesis, Proseminar

  Parareal is a parallel method for the numerical solution of ordinary differential equations in the time domain. It was originally developed by Lions and Maday and can be interpreted as a multigrid method in time or in terms of multiple shooting methods. The generalization to differential algebraic equations was just recently proposed. This project aims to further investigate this idea and to apply the methodology to challenging examples that are not “strangeness-free”. go

  Supervisors: Idoia Cortes Garcia, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps

  Announcement as PDF

• 2019

  Conventional finite element method and isogeometric analysis: a comparison

  Bachelor thesis

  Introduced in the early 2010, the isogeometric analysis (IGA) is a numerical technique for discretizing partial differential equations. The major advantage of IGA over other alternatives, such as the conventional finite element method (FEM) for instance, lies in its ability to represent exactly complex geometries. Indeed, while classical methods are relying on polynomial approximations of the computational domain, IGA directly exploits the non-uniform rational B-splines (NURBS) representation used in computer-aided design (CAD) tools. This unique feature allows IGA to reach a tremendous level of accuracy. Nonetheless, when comparing the resulting matrices, the FEM leads usually to more advantageous non-zero patterns. go

  Supervisors: Melina Merkel, B.Sc., Dr. Nicolas Marsic

  Announcement as PDF

• 2019

  Fast Adaptive Frequency Sweep for the Calculation of Scattering Parameters in the Frequency Domain

  Seminar paper, Bachelor thesis, Master thesis

  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. go

  Supervisors: PD Dr. rer. nat. Erion Gjonaj, Prof. Dr. rer. nat. Sebastian Schöps

  Announcement as PDF

• 2019

  Finite Element Tearing and Interconnect for Maxwell’s equations using IGA

  Seminar paper, Bachelor thesis, Master thesis

  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 go

  Supervisor: Prof. Dr. rer. nat. Sebastian Schöps

  Announcement as PDF

• 2019

  Efficient simulation of power converters using multirate partial differential equations

  Multiscale and multirate problems occur naturally in many applications from electrical engineering, e.g. buck converters. An efficient simulation can be achieved using the concept of Multirate Partial Differential Equations. go

  Supervisors: Andreas Pels, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps

  Announcement as PDF

• 2019

  Iterative Solvers for Complex Linear Systems

  Bachelor thesis

  The solution of systems of linear equations with complex valued coefficients is an important task for many simulation tasks in engineering. This thesis aims at implementing several important solvers that are not available in modern software libraries. go

  Supervisors: Felix Wolf, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps

  Announcement as PDF

• 2019

  Simulation of Electromigration Efffects in Electronic Devices

  Bachelor thesis, Master thesis

  In electronics, the most serious failure mechanism is due to electromigrationin the interconnects. This effect shall be modelled and simulated within an existing software environment. go

  Supervisors: Thorben Casper, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps

  Announcement as PDF

• 2019

  Adjoint-based Adaptivity for Uncertain HF Problems

  Seminar paper, Master thesis

  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. go

  Supervisors: Niklas Georg, M.Sc., Prof. Dr. rer. nat. Sebastian Schöps

  Announcement as PDF