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

Sivas, Abdullah A.; Southworth, Benjamin Scott; Rhebergen, Sander

doi:10.1137/20m1375103

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

Journal Article · Thu Sep 30 00:00:00 EDT 2021 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/20m1375103· OSTI ID:1827574

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Univ. of Waterloo, ON (Canada)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

This article 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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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE; Natural Sciences and Engineering Research Council of Canada (NSERC)

Grant/Contract Number:: 89233218CNA000001; RGPIN-05606-2015; B639443; B634212

OSTI ID:: 1827574

Report Number(s):: LA-UR-20-28396

Journal Information:: SIAM Journal on Scientific Computing, Vol. 43, Issue 5; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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

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