Information for master students

Contents

Graduating in the numerical analysis group (chair Prof.dr.ir. 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. GNN-based urban surrogate model for flood hazard quantification ( Deltares )
    for input from the TU Delft, please contact: Jing Zhao J.Zhao-9@tudelft.nl
  2. Realistic Computational Prototyping for Applied Electromagnetics
  3. Extracting turbulence statistics in large-scale two-phase flows using direct numerical simulation (NRG)
  4. Efficient solver for linear systems in CFD ( MARIN )
  5. QuadraFEM: Higher-order finite elements for complex geometries
  6. Numerical mathematics or scientific computing ( COMSOL )
  7. Realistic Computational Prototyping for Applied Electromagneics ( TNO )
  8. Machine Learning-Accelerated Solvers for Computational Fluid Dynamics Simulations ( TU Berlin )
  9. Geometry Learning for Complex Shaped Cells
  10. Nonlinear model reduction via invariant manifolds for high-dimensional IgA models
  11. AI-Enhanced PDE-based Parameterization Approach for Isogeometric Analysis
  12. Efficient and Reliable Hausdorff Distance Calculation for freeform NURBS models
  13. Unstructured graph based AI model for storm surge forecasting ( Deltares )
  14. Efficient Implementation of Supervised Learning with the Canonical Polyadic Decomposition on GPU
  15. Low Rank Tensor Approximation for Chebyshev Interpolation and Applications in Quantitative Finance
  16. Model-Order Reduction of Immersed Finite Element Systems
  17. Energy Transition: Modelling and Simulating Large Scale Multi-Carrier Energy Networks
  18. Armour Design using Machine Learning ( De Regt Marine Cables )
  19. Automatic Cable Drawing Generator ( De Regt Marine Cables )
  20. Domain Decomposition Techniques for the Helmholtz Equation - HPC Implementation
  21. Domain Decomposition Techniques for the Helmholtz Equation - Theoretical Investigation
  22. Improving performance of numerical methods for the shallow water equations on a GPU ( Deltares )
  23. Physics-compatible numerical methods for simulating wave damping by kelp farms
  24. Numerical techniques for efficiently solving a nonlinear model for salt intrusion in rivers
  25. Interactive waves for real-time ship simulation ( MARIN )
  26. The infinitesimal generator of Markovian SIS epidemics on a graph
  27. Improving Nonlinear Solver Convergence Using Machine Learning
  28. Implementation of unstructured high-order methods for spectral modelling of inhomogeneous ocean waves
  29. Direct numerical simulation of two-phase flows in nuclear reactors (NRG)
  30. Simulation of Energy-Autonomous regions (The Green Village)
  31. Error Estimates for Finite Element Simulations Using Neural Networks
  32. Iterative Sparse Solvers on the SX Aurora Vector Engine
  33. Overlapping Schwarz Domain Decomposition Methods for Implicit Ocean Models (Institute for Marine and Atmospheric Modeling)
  34. Accurate Hessian computation using smooth finite elements and flux preserving meshes: Solving the shallow water equations in estuaries
  35. Designing freeform optics for multiple source illumination with AI
  36. PDE-based grid generation techniques for industrial applications (City, University of London, PDM Analysis Ltd )
  37. 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:

Prof.dr.ir. Kees Vuik
Dr.ir. Martin van Gijzen
Dr. Neil Budko
Dr. Matthias Moller
Dr.ir. Artur Palha
Dr. Deepesh Toshniwal
Dr. Carolina Urzua Torres
Dr. Alexander Heinlein
Dr. Jonas Thies
Dr.ir. Vandana Dwarka
Dr.ir. Shobhit Jain
Dr.ir. Fang Fang
Dr.ir. Shuaiqiang Liu
Dr.ir. 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

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