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 coworkers) 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 coworkers), 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,
TNOTPD, 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.

Efficient pmultigrid solvers for Isogeometric Analysis

Parallel GPU solver for PLAXIS
(
Plaxis
)

Parallel multidomain Finite Elementbased computational tool for
variabledomain problems
(Alten )

Efficient simulation of steady twofluid flow

Stabilized finite element fluid flow modeling with
correct energy dissipation

Understanding the dynamics of
oscillating viscoelastic droplets

An integrated energy system on a national scale in 2050
(
Gasunie Transport Services B.V. (GTS)
)

Efficiently solving district heating network problems

Deflated preconditioned conjugate gradient method applied to genomic
evaluations
(
Wageningen UR
)

Advancing StateOf TheArt Cancer Care:
Student Projects in Proton Therapy
(
Holland Proton Therapy Centre
)

Performance comparison of implicit and explicit schemes for the shallow
water
equations on a GPU with FORTRAN90 code
(
Deltares
and
Stelling Hydraulics
)

Incorporating the DiscontinuousGalerkin method within DALES
(
KNMI
)

Isogeometric Analysis in Industrial
Turbomachinery Applications
(MTU Aero Engines, Munich, Germany)

Volumeconserving FEMbased levelset method

The contact model for wheel rail interaction
(Vortech)

There are a couple of MSc projects available within a collaboration
between the TU Delft and
Shell. The supervisor for these projects is: Johan Romate

NextGeneration Heat Recovery
"Noncondensable gas in twophase 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)

Energyefficient multigrid solution strategies and their application in
dataflow computing

Numerical methods for crowds

Traffic flow simulation: who takes the fast lane?

Fast Helmholtz solvers for seismic problems
(Shell)

Developing a modelling tool for offshore vessels
(Mocean offshore)

Fullwaveform inversion using an efficient frequencydomain
solver

Positivitypreserving RungeKutta Algebraic Flux Correction Schemes for Scalar
Conservation Laws with Discontinuous Fluxes
(TU Delft and
Shell
)

Numerical solution of a saddle point linear system
(
TU Delft: Department of Geoscience and Remote Sensing
)

Highperformance Computing for Topology Optimization

CFD  Thermal mixing
(NRG)

Mathematical Modeling of Plant Response to Environment
(HZPC)

Mathematics of SNPs to Phenotype Map
(HZPC)

CFD calibration of a flowmeter (VSL)

Preconditionering van het Multi Level Fast Multipole Algorithm
Verbetering van de efficiency van radarsignatuur analyse methoden
(Dutch)
(NLR)

Development of a full wave code for electron cyclotron wave propagation and absorption

Evaluating the EWI Wind Tunnel Performance

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
Prof.dr.ir. Kees Oosterlee
Dr.ir. Fred Vermolen
Dr.ir. Martin van Gijzen
Dr. Matthias Moller
Dr. Kristof Cools
Dr. Neil Budko
Dr. J. Romate
Dr.ir. D. den Ouden
 Mathematical Modeling of Plant Response to Environment
The influence of climate and other environmental conditions on the
growth and development of plants is an important subject in the
studies on sustainable agriculture. The
HZPC company
 a world leader in the marketing of seed
potatoes  is interested in developing a mathematical model of potato
growth in various conditions. They seek a model that could explain the
experimental data accumulated over approximately ten years about the
growth of different potato ?races? in various parts of the world. Such
a model would also help to evaluate and guide the breeding process.
The goal of this MSc project is to develop a firstprinciples dynamic
model of the potato growth starting from the seed and ending with the
harvest. The physical and chemical phenomena playing major role in
this process may range from solar radiation, temperature, availability
of water, and hardness of the soil, to the diffusion of chemicals
along the roots of the plant. An efficient, possibly, numerical,
method to solve the corresponding equations must be developed and the
results compared to the experimental data. The mathematical challenges
will involve: the formulation of a rigorous mathematical model,
solution of the diffusion equation and a moving boundary problem, as
well as equations of population dynamics.
The student who accepts this multidisciplinary challenge will be
stationed and guided at the group of Numerical Analysis at TU Delft
and have regular contact with the research staff at HZPC. The company
is also willing to provide some financial support to the student in
the form of an apprenticeship.
For further information contact:
Dr. F.J. Vermolen (f.j.vermolen@tudelft.nl)
Dr. N.V. Budko (n.v.budko@tudelft.nl)

Mathematics of SNPs to Phenotype Map
One of the main open problems in biology is the exact relation between
the genotype and the phenotype of the living organisms. In
mathematical biology this is known as the GP map problem. The HZPC
 a world leader in the marketing of
seed potatoes  has accumulated a large amount of experimental data on
both the genetic composition (SNPs  singlenucleotide polymorphisms) of
their potato "races" and the resulting properties of tubers that are
of interest to agriculture and commerce.
The goal of this MSc project is to develop a numerical algorithm to
retrieve the SNP to Phenotype map from the available data. The first
part of the project will consists of the literature study and a
rigorous formulation of the problem. The second part will be mainly
concerned with applying the methods of numerical linear algebra to the
solution of the problem.
The MSc student will be stationed and guided at the group of Numerical
Analysis at TU Delft and have regular contact with the research staff
at HZPC. The company is also willing to provide some financial support
to the student in the form of an apprenticeship.
For further information contact:
Dr. F.J. Vermolen (f.j.vermolen@tudelft.nl)
Dr. N.V. Budko (n.v.budko@tudelft.nl)
Previous Master projects
Below is a list of previous Master projects
 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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