2023/06/11 by Alexey Voronin, Voronin, Alexey, Scott MacLachlan +5 · 1 citation
Computer Science · Engineering · #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2306.06795
openalex publication_date 2023/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate a novel monolithic algebraic multigrid (AMG) preconditioner for the Taylor-Hood (\pmbℙ2/ℙ1) and Scott-Vogelius (\pmbℙ2/ℙ1disc) discretizations of the Stokes equations. The algorithm is based on the use of the lower-order \pmbℙ1iso\kern1pt\pmbℙ2/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 \pmbℙ1iso\kern1pt\pmbℙ2/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 is developed to improve parallelism. The preconditioner demonstrates robust performance across a variety of 2D and 3D 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.