{
  "abstract": "It is mathematically proved that, for a grid under a boundary-preserving piecewise-smooth deformation, the positivity of the Jacobian determinant in each closed element is also a sufficient condition for the deformed grid to remain valid. Most of the proof is devoted to showing that the element-wise positivity of the Jacobian indeed induces a local isomorphism in the grid-deformation setting. This result provides users of ALE methods and of the generalized Lagrangian method with a clean answer: checking the Jacobian alone is enough to determine the validity of the deformed grid.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18308",
  "author_total": 3,
  "authors": [
    {
      "name": "Yicun Zhen"
    },
    {
      "name": "Shouxian Zhu"
    },
    {
      "name": "Shipeng Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1sh55z8gr8vq0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18308",
  "fulltext_url": null,
  "id": "1sh55z8gr8vq0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18308",
  "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",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7213528729",
  "pdf_url": "https://arxiv.org/pdf/2609.18308",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1sh55z8gr8vq0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.18308",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18308"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "An efficient and rigorous criterion for the admissible time step of deforming grids in generalized Lagrangian and ALE methods",
  "title_text": "An efficient and rigorous criterion for the admissible time step of deforming grids in generalized Lagrangian and ALE methods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/1sh55z8gr8vq0",
  "venue": "arXiv",
  "versions": []
}