Abstract
Dynamical low-rank approximation (DLRA) is an emerging tool for reducing computational costs and provide memory savings when solving high-dimensional problems. In this work, we propose and analyze a semi-implicit dynamical low-rank discontinuous Galerkin (DLR-DG) method for the space homogeneous kinetic equation with a relaxation operator, modelling the emission and absorption of particles by a background medium. To ensure stability and to preserve important properties of the original model problem, careful construction of numerical methods for DLRA is necessary. Similar to the classical DG method, we show that the proposed DLR-DG method is well-posed. We also identify conditions such that the DLR-DG solution converges to the equilibrium. Numerical results are presented that demonstrate the theoretical findings.
