Dynamical low-rank approximation for the simulation of radiation heat waves (B09)

• Subject Area: Mathematics
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 258734477

This project aims at applying, adapting, and implementing the dynamical low-rank method for the simulation of radiation heat waves. We combine the method with a high-order Discontinuous Galerkin (DG) discretization in space, and either a spectral or collocation method in angle. The dynamical low-rank approximation leads to differential equations for factors in a decomposition of the solution, which need to be solved numerically. This approach seems particularly suitable for our purposes because in many relevant cases, the propagation of radiation heat waves can be described by an asymptotic limit equation. Thus, the effective dynamics take place on a lower-dimensional manifold. In this way, the six-dimensional (3 space, 2 angles, 1 frequency) radiation transport problem is reduced, both in computational cost as well as in-memory footprint. using hierarchical decompositions, we increase the efficiency of the dynamical low-rank method and investigate parallelization strategies.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1173: Wave phenomena: analysis and numerics
• Applicant Institution: Karlsruher Institut für Technologie
• Project Heads: Professor Dr. Martin Frank; Professor Dr. Christian Lubich, until 6/2023