AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion)

This paper investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in all-at-once solution space-time hybridizable discontinuous Galerkin (HDG) discretization advection-dominated flows. The motivation for this study is that time-dependent advection-diffusion equation can be seen "steady" problem $(d+1)$-dimensions AIR has been shown to robust solver steady problems. Numerical examples demonstrate effectiveness problems on fixed domains, using both slab-by-slab discretizations, context uniform adaptive mesh refinement. A closer look at geometric coarsening structure arises also explains why provide robust, scalable convergence advective hyperbolic problems, while most multilevel parallel-in-time schemes struggle with such