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:
- First, you inform Prof. Vuik (or one of the co-workers) and
discuss
the courses that will be included in your
graduation package.
- Some months before starting the Master's thesis you contact Prof.
Vuik
(or one of the co-workers), so that your wishes concerning the topic of
the
thesis can be included while searching a Master's project.
- After that we will look for a suitable place to carry out the
research.
Examples of research institutions include: Philips NatLab, Delft
Hydraulics,
TNO-TPD, Shell, academic hospitals etc.
It is, of course, also possible to stay at TUD and have a regular
contact
with a member of the numerical analysis group.
-
Initially, you perform a literature study to get a good overview of
the
topic you will work on. This study (duration: 3 months) is finalized
in a
written report and with a short presentation.
-
After this, the research starts, which ends in a Master's thesis and
with an
oral presentation. This final stage of the graduation takes about 6
months.

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.
-
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
(NRG)
-
Direct numerical simulation of two-phase flows in nuclear reactors
(NRG)
-
Solvers to model the structures of the subsurface
(Schlumberger)
-
An integrated benchmark model for SA-CCR (Standardized Approach for Counterparty Credit Risk)
(FF Quant)
-
Automation of year-round AC power flow calculations of the
European electricity grid
(TenneT)
-
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
(collaboration with
Hasselt University
)
-
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
(Sandia)
-
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
-
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
(HMC)
-
Double Wake implementation for
thick trailing edge wind turbine airfoils
(ECN)
-
Developing a modelling tool for offshore vessels
(Mocean offshore)
-
Solving
Integral Equations Faster using GPU's
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. Dennis den Ouden

Previous Master projects
Below is a list of previous Master projects
- 2022
- 2021
- 2020
- 2019
- 2018
- 2017
- 2016
- 2015
- 2014
- 2013
- 2012
- 2011
- 2010
- 2009
- 2008
- 2007
- 2006
- 2005
- 2004
- 2003
- 2002
- 2001

How to deal with computer problems?

Additional information
- Vacatures
- Women and Mathematics
European Women in Mathematics
is an international association of women
working in the field of mathematics in Europe.

Contact information:
Kees
Vuik
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