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. Interactive waves for real-time ship simulation ( MARIN )
  2. The infinitesimal generator of Markovian SIS epidemics on a graph
  3. Randomized Numerical Linear Algebra for Stable Space-Time Finite Element Methods (collaboration with University of Oxford)
    please contact Carolina Urzua-Torres ( c.a.urzuatorres@tudelft.nl ) for further details
  4. Enhancing Sea Ice Dynamics in the Climate System by Machine Learning
  5. Domain Decomposition for Machine Learning Based Medical Imaging
  6. Improving Nonlinear Solver Convergence Using Machine Learning
  7. Implementation of unstructured high-order methods for spectral modelling of inhomogeneous ocean waves
  8. Medical Image-to-Image Translation: Towards clinically accurate adversarial translation frameworks for medical applications (Genera (Generative Radiology))
  9. AI-driven turbulence modeling of two-phase flows in nuclear reactors (NRG)
  10. Direct numerical simulation of two-phase flows in nuclear reactors (NRG)
  11. Solvers to model the structures of the subsurface (Schlumberger)
  12. An integrated benchmark model for SA-CCR (Standardized Approach for Counterparty Credit Risk) (FF Quant)
  13. Automation of year-round AC power flow calculations of the European electricity grid (TenneT)
  14. Simulation of Energy-Autonomous regions (The Green Village)
  15. Error Estimates for Finite Element Simulations Using Neural Networks
  16. The Application of Neural Networks to Predict Skin Evolution After Burn Trauma (collaboration with Hasselt University )
  17. Iterative Sparse Solvers on the SX Aurora Vector Engine
  18. Block Preconditioners for Monolithic Solvers of Very Large Floating Structures
  19. Parallel Multiplicative One-Level Schwarz Preconditioners With FROSch and Trilinos (Sandia)
  20. Overlapping Schwarz Domain Decomposition Methods for Implicit Ocean Models (Institute for Marine and Atmospheric Modeling)
  21. Accurate Hessian computation using smooth finite elements and flux preserving meshes: Solving the shallow water equations in estuaries
  22. Designing freeform optics for multiple source illumination with AI
  23. PDE-based grid generation techniques for industrial applications (City, University of London, PDM Analysis Ltd )
  24. 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. 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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