{
  "abstract": "We prove, to our knowledge, the first unconditional cumulative closure estimates for the Arnold--Mukherjee--Pouly (AMP) refinement algorithm and the original face-marked tetrahedral algorithm of Bänsch on arbitrary conforming initial tetrahedral meshes. Let $T_0,\\ldots,T_L$ be an adaptive mesh sequence generated by either algorithm, with $M_\\ell\\subseteq T_\\ell$ denoting the marking set at step $\\ell$. Then $$\\#T_L-\\#T_0\\leq C_{\\mathrm{clos}}(T_0)\\sum_{\\ell=0}^{L-1}\\#M_\\ell.$$ The proof is intrinsic to the physical three-dimensional mesh and requires neither an initial compatibility condition nor a higher-dimensional embedding. It organizes conformity refinements into a causal forest and combines a uniform horizontal-propagation estimate with a weighted packing argument to obtain an explicit closure constant. For the original Bänsch algorithm, every history-dependent resolution of the initial two-edge ambiguity is represented by one of finitely many AMP histories. The estimate therefore holds uniformly for arbitrary deterministic or nondeterministic choices. This resolves a long-standing complexity question for the Bänsch--AMP family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29616",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuwen Li"
    },
    {
      "name": "Zhiyuan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9t6jqh9zhxr7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29616",
  "fulltext_url": null,
  "id": "e9t6jqh9zhxr7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29616",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
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      "arxiv",
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.29616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9t6jqh9zhxr7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29616"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Closure complexity of Bänsch-type algorithms for tetrahedral mesh refinement",
  "title_text": "Closure complexity of Bänsch-type algorithms for tetrahedral mesh refinement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/e9t6jqh9zhxr7",
  "venue": "arXiv",
  "versions": []
}