We assign topics for bachelor's and master's theses in the areas of inverse problems (theory and applications), optimization, tomographic imaging, mathematical modeling (e.g. for elastic and viscoelastic materials), inverse problems in engineering, to name only a few.
Bachelor's theses consist in general either of elaborating an article or special subjects in the area of numerical mathematics, or the implementation of numerical algorithms in small routines (preferable in C or Matlab).
Master's theses are also theoretical or practial assignments, but demand for a deeper understanding of the corresponding topic. Usually the assignment has a subject which is associated to the reserach areas of the working group, i.e. inverse problems, tomographic imaging, inverse elasticity or optimization. In this way master students gain insights to current research projects and are guided to scientific research.
Current theses topics:
- inversion techniques and algorithms in 2D and 3D vector tomography
- modeling of the measurement process in terahertz tomography
- contour reconstruction in terahertz tomography by thresholding
- sequential subspace optimization for nonlinear equations in Banach spaces
- model reduction for inverse problems based on elastic wave equations
- testing damage scenarios for hyperelastic materials
- ill-posedness of operator equations in Bochner spaces
- Gamma convergence of Tikhonov functionals
- ultrasound tomography and digital reconstruction for non-destructive testing of cultural, marmoreal assets (sketch of project), in cooperation with Fraunhofer IBMT
- regularization methods and machine learning
An assignment is possible at any time. Own suggestions are welcome.
Please contact Prof. Dr. Thomas Schuster.