AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion)
Abstract
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 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 advection-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.
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Published In
SIAM Journal on Scientific Computing
Pages: A3393 - A3416
DOI: 10.1137/20M1375103
ISSN (online): 1095-7197
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© 2021, Society for Industrial and Applied Mathematics.
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Submitted: 22 October 2020
Accepted: 7 June 2021
Published online: 30 September 2021
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Lawrence Livermore National Laboratory https://doi.org/10.13039/100006227 : B639443, B634212
Natural Sciences and Engineering Research Council of Canada https://doi.org/10.13039/501100000038 : RGPIN-05606-2015
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