Calculus of Variations and Geometric Measure Theory

PhD-position at TU-Vienna: numerical methods for highly oscillatory differential equations

created by arnold on 10 Dec 2019

Deadline: 16 dec 2019

- job vacancy in the research group of Anton Arnold, at TU Vienna, 30 hours per week
- start: 2.1.2020 (or soon after), 4 years
- annual gross salary: 30.077 EUR

Scientific topic: Numerical methods for highly oscillatory differential equations. The successful candidate will work on the project "Numerical methods for highly oscillatory differential equations", in a collaboration between TU Vienna, University of Vienna, and University of Bourgogne (Dijon).

Highly oscillatory scattering problems appear in many wave propagation models (from acoustics, electronics, quantum mechanics - e.g. Schrödinger equation in the classical limit). The goal of this project is to develop and analyze efficient numerical methods that do not need to resolve each oscillation.

Possible aspects of the PhD research include:
- hybrid (analytical-numerical) scheme for vector systems and 2D waveguides
- coupling of such WKB-based methods to the Landau-Zener formula close to eigenvalue crossings
- error analysis

Benefits: An association with the ongoing doctoral school "Dissipation and dispersion in nonlinear partial differential equations" is offered, for details see: http:/asc.tuwien.ac.at~npde
Thus the PhD candidate can benefit from the collaboration between the three universities through workshops, research stays, and courses. The candidate will be part of a network of researchers on all levels (PhD candidates, post-docs, professors) involved in the doctoral school.

Requirements: - completed master or diploma studies in mathematics
- solid knowledge of (partial) differential equations and numerical analysis; programming experience (e.g. Matlab)

The position comes with a teaching load of max. 4hweek (exercise classes). Initially teaching in English is OK.

Deadline: 16.12.2019 (or until position is filled) Application for position # 472.3.3:
via e-mail to katharina.pauschenwein@tuwien.ac.at