{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/monolithic-algebraic-multigrid","title":"Monolithic Algebraic Multigrid Preconditioners for the Stokes Equations","arxiv_id":"2306.06795","date":"2023-06-11","proceeding":null,"authors":["Alexey Voronin","Scott MacLachlan","Luke N. Olson","Raymond Tuminaro"],"abstract":"We investigate a novel monolithic algebraic multigrid (AMG) preconditioner for the Taylor-Hood ($\\pmb{\\mathbb{P}}_2/\\mathbb{P}_1$) and Scott-Vogelius ($\\pmb{\\mathbb{P}}_2/\\mathbb{P}_1^{disc}$) discretizations of the Stokes equations. The algorithm is based on the use of the lower-order $\\pmb{\\mathbb{P}}_1\\text{iso}\\kern1pt\\pmb{\\mathbb{P}}_2/\\mathbb{P}_1$ 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 $\\pmb{\\mathbb{P}}_1\\text{iso}\\kern1pt\\pmb{\\mathbb{P}}_2/\\mathbb{P}_1$ 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.","url_abs":"https://arxiv.org/abs/2306.06795v3","url_pdf":"https://arxiv.org/pdf/2306.06795v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"monolithic-algebraic-multigrid","repo_url":"https://github.com/alexey-voronin/monolithic_amg_for_stokes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}