Joint PhD and post-doc call of the SFB 65 "Taming Complexity in Partial Differential Systems"

Project Part in the SFB 65

Project Part 2 (Ansgar Jüngel) - link.

Type of position

Post-doc position.

Duration of employment

1 year (can be extended).

Affiliation

The successful applicant will be employed at the Institute of Analysis and Scientific Computing of TU Wien (Vienna, Austria) and will be associated to the workgroup of Ansgar Jüngel.

Theme

Solutions to diffusion equations usually possess some properties reflecting the physical or biological context, such as positivity, conservation of mass, exponential decay to equilibrium, or dissipation of energy/entropy. The aim of this research is to design numerical schemes for parabolic diffusion systems that satisfy these properties on the discrete level. These schemes are called structure preserving. An important tool to achieve this goal is the entropy method. We aim to develop and analyze discrete versions of this method.
Design efficient numerical approximations of (cross-diffusion) Maxwell-Stefan-Fourier systems, which model gas mixtures under thermal influence. Possible approaches are finite-volume, discontinuous Galerkin, or space-time techniques. Another topic is the discretization of spin drift-diffusion systems, which describe the spin-polarized transport of electrons in semiconductors. The tasks are the existence of discrete solutions, proof of the structure-preserving properties, convergence of the scheme, and numerical implementation of the scheme in one and two space dimensions.
PhD in Mathematics or related fields. Solid background in the theory of nonlinear partial differential equations and their numerical approximation. General knowledge of functional analytical techniques that are necessary for the numerical analysis. Convincing publication record in numerical analysis.

Involved researchers of the SFB

Ansgar Jüngel (TU Wien).

Preferred start date

As soon as possible.

Contact

For queries on this advertisement, please contact Prof. Ansgar Jüngel at juengel@tuwien.ac.at.

Requested documents

• A single pdf with CV and list of publications.
• A motivation letter.
• A pdf or a link to the PhD thesis.

Additional requested information

• Contact details of 2 possible references who will be ready to write a recommendation letter (we are not currently collecting recommendation letters, we will contact these 2 people only for the candidates in the short list if need be).

Online application

link