{
  "abstract": "Geometric multigrid methods for conforming finite element discretisations classically require a nested mesh hierarchy, forcing coarse meshes to be conforming, which is unsuitable for general domains. In order to eliminate this geometric constraint, we introduce and analyse a family of multilevel auxiliary space preconditioners. At the first level, a conforming Lagrangian discretisation on a fine simplicial mesh is preconditioned by a non-conforming polytopal discretisation posed on an arbitrarily agglomerated coarse mesh. At the subsequent levels, the coarse problem is solved by a geometric multigrid method for that polytopal discretisation on further agglomerated meshes, so that the whole hierarchy is generated from the fine mesh by agglomeration alone. We consider two polytopal discretisations, a symmetric interior penalty discontinuous Galerkin method and a hybrid high-order method. The prolongation operator at the first level is an element-wise interpolation onto the fine mesh followed by nodal averaging, preceded in the hybrid high-order case by a local potential reconstruction. For point-Jacobi and vertex-star patch additive Schwarz smoothers, we prove that the condition number of the preconditioned system is bounded by $O((H/h)^3)$, where $H/h$ is the coarsening ratio, and by $O((H/h)^2)$ for the DG variant with penalty proportional to $H/h$. Numerical experiments in two and three dimensions, on structured and unstructured meshes with agglomerates generated by automatic clustering algorithms, confirm the robustness of the preconditioners.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06012",
  "author_total": 2,
  "authors": [
    {
      "name": "Santiago Badia"
    },
    {
      "name": "Jordi Manyer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9myafqtpattr8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06012",
  "fulltext_url": null,
  "id": "9myafqtpattr8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06012",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06012",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9myafqtpattr8.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06012",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06012"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Geometric Multigrid Preconditioners for conforming Finite Element Methods on Arbitrarily Agglomerated Meshes",
  "title_text": "Geometric Multigrid Preconditioners for conforming Finite Element Methods on Arbitrarily Agglomerated Meshes",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:14Z",
  "url": "https://research.draconitic.com/paper/9myafqtpattr8",
  "venue": "arXiv",
  "versions": []
}