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PhD (f/m) in Efficient discretization schemes for linear kinetic equation
Veröffentlicht am(vor 1064 Tagen)
Bewerbungsende(vor 1026 Tagen)
University of TwenteEnschede (Niederlande)
PhD in Efficient discretization schemes for linear kinetic equation
38.0 hours per week
€ 2191 - € 2801
University of Twente (UT)
Linear kinetic equations describe the evolution of a probability density of particles within phase-space, i.e., independent
variables are space, time and velocity. Besides transport of particles, the main governing physical processes are absorption
and scattering at inhomogeneities and anisotropic structures. This type of equation has numerous applications, e.g., radiation
calculations in astronomy and medical treatments, medical imaging, and the design of semiconductors. Due to its importance and
wide applicability a lot of research has been conducted both in the analysis as well as in the numerical approximation of this
class of equations. Particularly, since it is almost always impossible to give analytic solutions, the numerical approximation
of solutions to the radiative transfer equation is of great importance for the aforementioned applications. Mathematically
the numerical approximation is still challenging due to the high-dimensionality and anisotropy of the problem. In particular,
the presence of transport regimes, fluidic regimes and diffusive regimes requires methods which are robust in treating this
multiscale problem. Particular emphasis is put on so-called ’compatible’ schemes which respect physical properties as, e.g.,
positivity of the solution, and mass conservation. The design of such methods is currently an active topic of research.
In this project the successful applicant should design new numerical methods for the efficient numerical solution of the
radiative transfer equation as a prototype for other applications mentioned above. This will include the development of
an efficient highly parallelized numerical solver which is applicable to problems in optical imaging.
Different research questions that are key to this project are:
Development of exterior calculus for this class of equations aiming at the systematic design of stable numerical approximation schemes.
Development of compatible discretizations, which in particular ensure positivity of the solution and mass conservation.
Development of reduced order models to break the curse of dimesionality and which allow for efficient large-scale computations
Ideally, several of the above posed questions are solved by the applicant and are implemented in a state-of-the art computer code.
For this work we are looking for MSc students having or will graduate(d) in one of the following subjects:
We expect the candidate to have excellent command of the English language as well as professional communication and team working skills.
For further information you can contact Prof. dr. Bernard Geurts firstname.lastname@example.org or Dr. Matthias Schlottbom
Candidates are invited to upload their application at the UT web address, including a short motivation letter, references (at least 2),
and CV to the application button below, before 01 May 2017.
Conditions of employment
The University of Twente offers a stimulating work environment in an area of applied, forefront research. You will have a full time
employment contract for the duration of 4 years and can participate in all employee benefits the UT offers. The gross monthly salary
starts with € 2.191,- in the first year and increases to € 2.801,- in the fourth year employment. Additionaly, the University
of Twente provides excellent facilities for professional and personal development, a holiday allowance (amount to 8%) and an end of
year bonus of 8.3%. A high-quality training programme is part of the agreement. The research has to result in a PhD thesis at the
end of the employment period.
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