Information for master students


Graduating in the numerical analysis group (chair C. Vuik).
In the investigation of physical, biological and economical phenomena numerical mathematics and computer simulations play an important role. As an example, we show a detail of the blood flow near a heart valve (video 1 and video 2).

In order to simulate such phenomena, a mathematical model of the reality is set up. Mathematical research is necessary to validate such a model. For this, results, principles and techniques from mathematical analysis are often used. The model should, of course, be an adequate representation of the reality. The necessary knowledge to judge this may be obtained from mathematical physics (biology, economy). Numerical mathematics is then the basis to solve the mathematical model efficiently and accurately. The solution is typically obtained by a computer simulation.

During a graduation at the chair for numerical analysis, the topics analysis, mathematical physics, linear algebra are treated. Most important is, however, the numerical analysis. The Master's thesis research can take place in a variety of topics in numerical mathematics, for example, in reducing numerical errors (of a problem's discretization, for example), or to improve the efficiency of a solution process, to analyse the convergence behaviour of an iterative solution method, or in parallel computing. The numerical questions always arise from practical applications.

If you would like to graduate in the numerical analysis group, the typical procedure is as follows:

Possibilities for Master projects
At this moment there are a number of Master projects available. It is possible to formulate new projects, where we take wishes of a masters student into account.
  1. Machine Learning-Accelerated Solvers for Computational Fluid Dynamics Simulations ( TU Berlin )
  2. Geometry Learning for Complex Shaped Cells
  3. Nonlinear model reduction via invariant manifolds for high-dimensional IgA models
  4. AI-Enhanced PDE-based Parameterization Approach for Isogeometric Analysis
  5. Efficient and Reliable Hausdorff Distance Calculation for freeform NURBS models
  6. Unstructured graph based AI model for storm surge forecasting ( Deltares )
  7. Efficient Implementation of Supervised Learning with the Canonical Polyadic Decomposition on GPU
  8. Low Rank Tensor Approximation for Chebyshev Interpolation and Applications in Quantitative Finance
  9. Model-Order Reduction of Immersed Finite Element Systems
  10. Energy Transition: Modelling and Simulating Large Scale Multi-Carrier Energy Networks
  11. Armour Design using Machine Learning ( De Regt Marine Cables )
  12. Automatic Cable Drawing Generator ( De Regt Marine Cables )
  13. Domain Decomposition Techniques for the Helmholtz Equation - HPC Implementation
  14. Domain Decomposition Techniques for the Helmholtz Equation - Theoretical Investigation
  15. Power Cable Temperature Reconstruction From Electromagnetic Reflectometry Data ( Alliander )
  16. Improving performance of numerical methods for the shallow water equations on a GPU ( Deltares )
  17. Physics-compatible numerical methods for simulating wave damping by kelp farms
  18. Numerical techniques for efficiently solving a nonlinear model for salt intrusion in rivers
  19. Interactive waves for real-time ship simulation ( MARIN )
  20. The infinitesimal generator of Markovian SIS epidemics on a graph
  21. Improving Nonlinear Solver Convergence Using Machine Learning
  22. Implementation of unstructured high-order methods for spectral modelling of inhomogeneous ocean waves
  23. Direct numerical simulation of two-phase flows in nuclear reactors (NRG)
  24. Automation of year-round AC power flow calculations of the European electricity grid (TenneT)
  25. Simulation of Energy-Autonomous regions (The Green Village)
  26. Error Estimates for Finite Element Simulations Using Neural Networks
  27. Iterative Sparse Solvers on the SX Aurora Vector Engine
  28. Overlapping Schwarz Domain Decomposition Methods for Implicit Ocean Models (Institute for Marine and Atmospheric Modeling)
  29. Accurate Hessian computation using smooth finite elements and flux preserving meshes: Solving the shallow water equations in estuaries
  30. Designing freeform optics for multiple source illumination with AI
  31. PDE-based grid generation techniques for industrial applications (City, University of London, PDM Analysis Ltd )
  32. Several projects on image and data analysis are available at the Academisch Borstkankercentrum of Erasmus MC
    Contact: Martin van Gijzen
For further information about these project and graduation at the chair Numerical Analysis we refer to: Kees Vuik Martin van Gijzen
Dr. Neil Budko
Dr. Matthias Moller Artur Palha
Dr. Deepesh Toshniwal
Dr. Carolina Urzua Torres
Dr. Alexander Heinlein
Dr. Jonas Thies Vandana Dwarka Shobhit Jain Fang Fang Shuaiqiang Liu Dennis den Ouden

Previous Master projects
Below is a list of previous Master projects

How to deal with computer problems?

Additional information

Contact information: Kees Vuik

Back to the home page or educational page of Kees Vuik