@article{abaf500b938648f6886bc39c3fbbecc0,
title = "MONOLITHIC ALGEBRAIC MULTIGRID PRECONDITIONERS FOR THE STOKES EQUATIONS",
abstract = "We investigate a novel monolithic algebraic multigrid (AMG) preconditioner for the Taylor-Hood (ℙ2/ℙ1) and Scott-Vogelius (ℙ2/ℙdisc1 ) discretizations of the Stokes equations. The algorithm is based on the use of the lower-order ℙ1 isoℙ2/ℙ1 operator within a defect-correction setting, in combination with AMG construction of interpolation operators for velocities and pressures. The preconditioning framework is primarily algebraic, though the ℙ1 isoℙ2/ℙ1 operator must be provided. We investigate two relaxation strategies in this setting. Specifically, a novel block factorization approach is devised for Vanka patch systems, which significantly reduces storage requirements and computational overhead, and a Chebyshev adaptation of the LSC-DGS relaxation from [54] is developed to improve parallelism. The preconditioner demonstrates robust performance across a variety of two-dimensional and three-dimensional Stokes problems, often matching or exceeding the effectiveness of an inexact block triangular (or Uzawa) preconditioner, especially in challenging scenarios such as elongated-domain problems.",
keywords = "algebraic multigrid, LSC-DGS relaxation, monolithic multigrid, Scott-Vogelius, Stokes equations, Vanka relaxation",
author = "Alexey Voronin and Scott Maclachlan and Olson, \{Luke N.\} and Tuminaro, \{Raymond S.\}",
note = "The work of the second author was partially supported by an NSERC Discovery Grant. The fourth author was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology \& Engineering Solutions of Sandia, LLC (NTESS), a wholly owned subsidiary of Honeywell International for the U.S. Department of Energy's National Nuclear Security Administration (DOE/NNSA) under contract DE-NA0003525. This written work is authored by an employee of NTESS. The employee, not NTESS, owns the right, title, and interest in and to the written work and is responsible for its contents. Any subjective views or opinions that might be expressed in the written work do not necessarily represent the views of the U.S. Government. The publisher acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this written work or allow others to do so, for U.S. Government purposes. The DOE will provide public access to results of federally sponsored research in accordance with the DOE Public Access Plan.",
year = "2025",
doi = "10.1137/23M1584514",
language = "English (US)",
volume = "47",
pages = "A343--A373",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",
}