AIR algebraic multigrid for a space-time hybridizable discontinuous Galerkin discretization of advection(-diffusion) [article]

Abdullah A. Sivas, Ben S. Southworth, Sander Rhebergen
2020 arXiv   pre-print
This paper investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a space-time hybridizable discontinuous Galerkin (HDG) discretization of advection-dominated flows. The motivation for this study is that the time-dependent advection-diffusion equation can be seen as a "steady" advection-diffusion problem in (d+1)-dimensions and AIR has been shown to be a robust solver for steady
more » ... ion-dominated problems. Numerical examples demonstrate the effectiveness of AIR as a preconditioner for advection-diffusion problems on fixed and time-dependent domains, using both slab-by-slab and all-at-once space-time discretizations, and in the context of uniform and space-time adaptive mesh refinement. A closer look at the geometric coarsening structure that arises in AIR also explains why AIR can provide robust, scalable space-time convergence on advective and hyperbolic problems, while most multilevel parallel-in-time schemes struggle with such problems.
arXiv:2010.11130v2 fatcat:nipeoeqyfvbapdm64vqvkoxsie