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:
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
Parallel Multiplicative One-Level Schwarz Preconditioners With FROSch and Trilinos
Overlapping Schwarz Domain Decomposition Methods for Implicit Ocean Models
(Institute for Marine and Atmospheric Modeling)
Reduced Order Models for Fluid Flow With Generative Adversarial Networks (GANs)
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
Coercive Space-Time Boundary Element Methods
for the Acoustic Wave Equation
Preconditioning for Scattering by Multi-screens
Improvement of the algorithms of ASA (Advanced Semiconductor Analysis) software
High-order accurate and stable material point method
Efficient simulation of steady two-fluid flow
Stabilized finite element fluid flow modeling with
correct energy dissipation
Efficiently solving district heating network problems
Next-Generation Heat Recovery
"Non-condensable gas in two-phase dynamic simulation"
(NEM Energy B.V.)
Distributed Alternating Current (AC) power flow with limited information
Efficient computation of slamming loads through zonal modeling
Double Wake implementation for
thick trailing edge wind turbine airfoils
Fast Helmholtz solvers for seismic problems
Developing a modelling tool for offshore vessels
Integral Equations Faster using GPU's
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. 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