Topics for thesises

Preliminary remark

My main research area is the numerics of partial differential equations (PDEs) with an emphasis on the practical implementation of solvers. On the other hand, I’m interested in quite a wide range of topics. For example, I have supervised also thesises in set theory, glacier simulation, software engineering, and social choice theory.

An important speciality of my research is that I use the programming language Common Lisp (CL) for scientific computing. Exaggerating only mildly one can describe CL as a programming language which is waiting for almost 30 years at a position in programming language space which modern languages are heading for. So if you are interested in doing something which is surely not in the mainstream, you are at the right place here.

List of topics

Difficulty: [P]=Project, [B]=Bachelor, [M]=Master, [D]=Dissertation

Emphasis on implementation

• [PB] Android: Port Femlisp to ECL on Android.
• [PB] AVX: Implement a direct solver in Common Lisp with AVX vector operations
• [PB] Web server: Make a webserver which performs all Femlisp demos
• [BM] Flexible matrix-vector format: At the moment, Femlisp uses a block format where blocks are indexed by the geometric entity. This allows for simultaneous local changes in mesh and matrix, but implies a severe performance hit. Make both the vector and matrix format selectable and improve performance drastically in this way.
• [BM] VTK graphics: Implement interactive graphics with VTK instead of DX which is used at the moment.
• [MD] Matrix-less calculations Implement matrix-less solving of PDEs.
• [MD] HDG: Implement locally structured (HDG) Finite Elements.
• [MD] Discontinuous Galerkin: Integrate Discontinuous Galerkin methods.
• [MD] Finite Volume Method Integrate Finite Volume methods.
• [PBMD] Fast calculation of aircraft polars: We have a working 2D solution which can be improved in several directions.
• [PBMD] Tutorials: Port some further Deal.II tutorials to Femlisp.

Emphasis on theory

• [PBM] Cahn-Hilliard-Gleichung – Numerical Treatment of the Cahn-Hilliard equation
• [PBM] Streamline-diffusion methods – Treatment of convection-dominated flow problems
• [MD] Multiscale Finite Elements – Theory and implementation
• [MD] Multiscale-Monte-Carlo-Methods – Theory and Implementation
• [MD] Multigrid for Discontinuous Galerkin
• [MD] Dimensional reduction for chemical processes