Information for master students
Graduating in the numerical analysis group (chair Prof.dr.ir. C.
In the investigation of physical, biological and economical phenomena
numerical mathematics and computer simulations play an important role.
example, we show a detail of the blood flow near a heart valve
In order to simulate such phenomena, a mathematical model of the
set up. Mathematical research is necessary to validate such a model.
For this, results, principles and techniques from mathematical analysis
often used. The model should, of course, be an adequate representation
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
During a graduation at the chair for numerical analysis, the topics
mathematical physics, linear algebra are treated. Most important is,
the numerical analysis. The Master's thesis research can take place in
variety of topics in numerical mathematics, for example, in reducing
numerical errors (of a problem's discretization, for example), or to
the efficiency of a solution process, to analyse the convergence
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:
- First, you inform Prof. Vuik (or one of the co-workers) and
the courses that will be included in your
- Some months before starting the Master's thesis you contact Prof.
(or one of the co-workers), so that your wishes concerning the topic of
thesis can be included while searching a Master's project.
- After that we will look for a suitable place to carry out the
Examples of research institutions include: Philips NatLab, Delft
TNO-TPD, Shell, academic hospitals etc.
It is, of course, also possible to stay at TUD and have a regular
with a member of the numerical analysis group.
Initially, you perform a literature study to get a good overview of
topic you will work on. This study (duration: 3 months) is finalized
written report and with a short presentation.
After this, the research starts, which ends in a Master's thesis and
oral presentation. This final stage of the graduation takes about 6
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.
For further information about these project and graduation at the chair
Numerical Analysis we refer to:
Improving performance of numerical methods for the shallow water equations on a
Compressible vs. incompressible pore water in fully-saturated
Physics-compatible numerical methods for simulating wave damping by kelp farms
Numerical techniques for efficiently
solving a nonlinear model for salt intrusion in rivers
Interactive waves for real-time ship simulation
The infinitesimal generator of Markovian SIS epidemics on a graph
Randomized Numerical Linear Algebra for Stable Space-Time Finite Element Methods (collaboration with
University of Oxford)
please contact Carolina Urzua-Torres ( firstname.lastname@example.org ) for further details
Improving Nonlinear Solver Convergence Using Machine Learning
Implementation of unstructured high-order methods for spectral modelling of inhomogeneous ocean waves
Medical Image-to-Image Translation: Towards clinically accurate adversarial translation
frameworks for medical applications
(Genera (Generative Radiology))
AI-driven turbulence modeling of two-phase flows in nuclear reactors
Direct numerical simulation of two-phase flows in nuclear reactors
Solvers to model the structures of the subsurface
An integrated benchmark model for SA-CCR (Standardized Approach for Counterparty Credit Risk)
Automation of year-round AC power flow calculations of the
European electricity grid
Simulation of Energy-Autonomous regions
(The Green Village)
Error Estimates for Finite Element
Simulations Using Neural Networks
The Application of Neural Networks to Predict Skin
Evolution After Burn Trauma
Iterative Sparse Solvers on the SX
Aurora Vector Engine
Block Preconditioners for Monolithic
Solvers of Very Large Floating Structures
Overlapping Schwarz Domain Decomposition Methods for Implicit Ocean Models
(Institute for Marine and Atmospheric Modeling)
Accurate Hessian computation using smooth finite elements
and flux preserving meshes:
Solving the shallow water equations in estuaries
Designing freeform optics for multiple source illumination with AI
PDE-based grid generation techniques for industrial applications
(City, University of London,
PDM Analysis Ltd
Several projects on image and data analysis are available at the
Academisch Borstkankercentrum of Erasmus MC
Contact: Martin van Gijzen
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?
- Women and Mathematics
European Women in Mathematics
is an international association of women
working in the field of mathematics in Europe.
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educational page of Kees Vuik