Doctoral Researcher (f/m/d) Project B9 “Dynamical low-rank approximation for the simulation of...

Area of research:

PHD Thesis

Part-Time Suitability:

The position is suitable for part-time employment.

Starting date:

08.09.2021

Job description:

The CRC has been funded by the German Research Foundation (DFG) since 2015. Its goal is to analytically understand, numerically simulate, and eventually manipulate wave propagation under realistic scenarios by intertwining analysis and numerics.

The Project B9 “Dynamical low-rank approximation for the simulation of radiation heat waves” (https://www.waves.kit.edu/B9.php ) aims at applying, adapting, and implementing the dynamical low-rank method for the simulation of radiation heat waves. We combine the dynamical low-rank method with a high-order Discontinuous Galerkin (DG) discretization in space, and either a spectral or collocation method in angle. The ansatz functions are tensorized so that one can interpret the semi-discretization in space, angle, and frequency as a tensor-valued ordinary differential equation in time. The dynamical low-rank approximation is a low-rank factorization updating technique. It leads to differential equations for factors in a decomposition of the solution, which need to be solved numerically. The dynamical low-rank method seems particularly suitable for our purposes, because in many relevant test cases the propagation of radiation heat waves can be described by an asymptotic limit equation. Thus, the effective dynamics takes place on a lower-dimensional manifold. In this way, the six-dimensional (3 space, 2 angle, 1 frequency) radiation transport problem is reduced, both in computational cost as well as in memory footprint.

We seek a doctoral researcher with strong interest in numerical mathematics and high-performance computing. You will develop modifications of the dynamical low-rank method to enforce the numerical scheme's conservation of the overall energy and mass of particles, and to make the scheme asymptotic-preserving. A special focus will be on the investigation of parallelization strategies so that we obtain an efficient high-performance computing (HPC) implementation. Together with application scientists you perform simulations of radiation heat waves in realistic application test cases and especially investigate the memory use of the new method. You will have the opportunity to attend conferences, workshops and summer schools. Engagement in teaching is encouraged.

We provide an inspiring, attractive, interdisciplinary, and internationally recognized scientific environment with access to excellent facilities of the KIT, a wide scope of advanced training options within our integrated research training group, and flexible working time models. Our CRC aims at the implementation of equal opportunities, it promotes diversity and supports persons with childcare or eldercare responsibilities as well as persons with disabilities. Funds for travel and guests are available through the CRC.

This research center is part of the Helmholtz Association of German Research Centers. With more than 42,000 employees and an annual budget of over € 5 billion, the Helmholtz Association is Germany's largest scientific organisation.