Dr. Matthias Schlottbom (universitaet Muenster)


Date: 01 JuneĀ  2016
Time: 12:45 - 13:30 (Lunch available from 12:35)
Room:RA 1501 (Ravelijn)


Title: On Galerkin schemes for time-dependent radiative transfer

Abstract:

Joint work with Herber Egger (TU Darmstadt)
The numerical solution of time dependent radiative transfer problems is challenging, both, due to the high dimension and the anisotropic structure of the underlying integro-partial differential equation. Starting from an appropriate variational formulation, we propose a general strategy for designing numerical methods based on a Galerkin discretization in space and angle combined with appropriate time stepping schemes. This allows us to systematically incorporate boundary conditions and to inherit basic properties like exponential stability from the continuous level. We also present the basic approximation error estimates. The starting point for our considerations is to rewrite the radiative transfer problem as a system of evolution equations which has a similar structure as more standard rst order hyperbolic systems in acoustics or electrodynamics. This allows us to generalize the main arguments of the numerical analysis of such applications to the radiative transfer problems under investigation. We also discuss a particular discretization scheme based on a truncated spherical harmonic expansion in angle and a nite element discretization in space.