{
  "abstract": "We propose a new fractional threshold-dynamics algorithm for subdiffusive interface motion and apply it to multiphase grain-growth simulations. The method combines the L1 discretization of the Caputo time derivative with a Helmholtz-resolvent thresholding step. At each time level, the L1 convolution produces a convex history average of the previously thresholded states; this history-dependent field is then propagated by a Helmholtz diffusion solve and projected back to pure phases by thresholding. For $α=1$, the method reduces to a Helmholtz-resolvent analogue of the Merriman-Bence-Osher scheme, whereas for $0<α<1$ it introduces a subdiffusive temporal memory. We establish a variational characterization, maximum and comparison principles, and stability for the continuous Helmholtz diffusion step. We also derive a memory-tail estimate and a finite-dimensional pinning criterion under an explicit resolvent-contraction hypothesis. The equal-tension multiphase scheme is implemented on periodic grids. The numerical experiments investigate the joint influence of the L1 history and the smoothing length. The fixed-step runs show faster coarsening for smaller fractional orders in the tested regime, while a comparison at fixed smoothing length examines the influence of the L1 history on successive updates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07938",
  "author_total": 1,
  "authors": [
    {
      "name": "Marvin Fritz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9jsjgwzqfe52v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07938",
  "fulltext_url": null,
  "id": "9jsjgwzqfe52v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07938",
  "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"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2505|Solidification and crystal growth phenomena"
    ]
  ],
  "openalex": "W7212066693",
  "pdf_url": "https://arxiv.org/pdf/2609.07938",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9jsjgwzqfe52v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07938",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07938"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Threshold dynamics for subdiffusive grain growth",
  "title_text": "Threshold dynamics for subdiffusive grain growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/9jsjgwzqfe52v",
  "venue": "arXiv",
  "versions": []
}