Student projects
The following possible project topics are categorized into Master, Bachelor thesis topics and scientific computing practical topics. However, with adaptations the topics may also be considered for a different purpose. Some of the projects have a detailed description already (on the linked page). To learn about the others and possible alternatives please directly contact us (C. Lehrenfeld). Many of these projects involve programming tasks. To learn more about the related software packages, have a look at the software page.
Master thesis projects:
Open:
- Weak Trefftz DG methods (analysis, unfitted Trefftz DG, ..)
- Trefftz DG methods for Stokes equations
- (Weak and embedded) Trefftz DG methods for linear advection equations
- Numerical solution of a vectorial model problem of solar oscillations [1 project finished, more possible]
Reserved or currently ongoing:
- Discretization of incompressible flows on moving surfaces [ongoing]
- A combination of Trefftz DG and Trace-DG for Stokes problems on unfitted Surfaces
- Weak Trefftz DG methods for Space-Time Discretizations
Finished theses:
A list of former Master's theses can be found here.
Bachelor thesis projects:
Open:
- unfitted space time discretization for Stokes and Navier-Stokes flow on moving domains
- Trefftz DG methods
- Preconditioning of a Helmholtz-Beltrami operator on a sphere
Reserved or currently ongoing:
- Variational methods for solving ODEs [ongoing]
Finished theses:
A selection of former Bachelor's theses can be found here.
Scientific computing practical projects:
General topics (for students without a strong background in numerics of PDEs):
- Reinitialization/Redistancing of level set functions with k-d-trees [
pythonorC++] - Implementation of an ODE-solver framework for implicit-explicit time integration schemes [
python] - time-adaptivity with space-time discretizations of parabolic PDEs [
python] - OLTEM (optimal local truncation error method) : a modified finite difference method for solving PDEs [
pythonor any language]
Reserved or currently ongoing:
- Machine learning for the extraction of boundary layer profiles based on local flow data in CFD [
python] [ongoing] - Navier-Stokes equations with stochastic excitation [
python] [ongoing] - Implementation of Krylov subspace solvers with Multipreconditioning techniques [
python] [ongoing] - Coupling Navier-Stokes and scalar transport equations [ongoing]
- Implementation of a pedestrian flow problem [
python] [ongoing] - Implementation of optimizations and conversions for sparse matrix formats [
C++] [ongoing]
More advanced topics (for students with background in numerics of PDEs):
- Shape Optimization for CFD
- Inverse Problems in PDEs
- Implementation of an unsteady incompressible Two-phase flow solver
- SIMD vectorization of finite element operations in the software package
ngsxfem - Model templates for unfitted discretizations for a class of two-phase flow problems
- Integration of an aggregated unfitted FEM approach into
ngsxfem - Integration of DG integrals in an unfitted space-time cut geometry setting (with integration in
ngsxfem)
Reserved or currently ongoing:
- Control of shape regularity in isoparametric finite elements through Bernstein basis representations