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.

Improving performance of numerical methods for the shallow water equations on a
GPU
(
Deltares
)

Compressible vs. incompressible pore water in fullysaturated
poroelastic soil
(
Rijkswaterstaat WVL)

Physicscompatible 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 realtime ship simulation
(
MARIN
)

The infinitesimal generator of Markovian SIS epidemics on a graph

Randomized Numerical Linear Algebra for Stable SpaceTime Finite Element Methods (collaboration with
University of Oxford)
please contact Carolina UrzuaTorres ( c.a.urzuatorres@tudelft.nl ) for further details

Improving Nonlinear Solver Convergence Using Machine Learning

Implementation of unstructured highorder methods for spectral modelling of inhomogeneous ocean waves

Medical ImagetoImage Translation: Towards clinically accurate adversarial translation
frameworks for medical applications
(Genera (Generative Radiology))

AIdriven turbulence modeling of twophase flows in nuclear reactors
(NRG)

Direct numerical simulation of twophase flows in nuclear reactors
(NRG)

Solvers to model the structures of the subsurface
(Schlumberger)

An integrated benchmark model for SACCR (Standardized Approach for Counterparty Credit Risk)
(FF Quant)

Automation of yearround AC power flow calculations of the
European electricity grid
(TenneT)

Simulation of EnergyAutonomous 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

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

PDEbased 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
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
 2023
 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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