{
  "abstract": "Mesh adaptation reduces the cost of simulations with localized solution features, but repeated adaptation can become prohibitive in parametric studies. Selecting a precomputed library mesh may be insufficient when the refined region moves with the operating condition. We introduce transport-based mesh interpolation (TMI), which constructs an adapted mesh for a queried parameter by interpolating nearby meshes from an offline library. Each dyadic mesh is represented by the empirical measure of its cell centers, encoding refinement patterns through spatial point density. The interpolated representative is defined as the transport barycenter of neighboring mesh measures, using parametric barycentric weights. Geometric rules then reconstruct an admissible dyadic mesh from this representative. The proof-of-concept implementation uses a sliced Wasserstein approximation for simplicity and efficiency. Projection experiments on moving hyperbolictangent cuts isolate interpolation and reconstruction behavior, while a reaction-diffusion problem with a moving triangular source evaluates PDE-adapted meshes. In the tested configurations, the depth-informed and max-one-point reconstructions produce meshes with errors consistent with direct adaptation, with a favorable accuracy-size compromise for the depth-informed variant. Moreover, amortized online TMI becomes faster than full adaptation for the finest tested tolerances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Hugo Dornier"
    },
    {
      "name": "Olivier Le Maitre"
    },
    {
      "name": "Pietro Marco Congedo"
    },
    {
      "name": "Théotime Niault"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8v6qx6hmswjyq.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "8v6qx6hmswjyq",
  "issns": [],
  "landing_url": "https://hal.science/hal-05802486v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.spi"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "hal",
      "1.math.math-na"
    ],
    [
      "hal",
      "1.spi.meca"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05802486/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8v6qx6hmswjyq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05802486",
      "source": "hal",
      "url": "https://hal.science/hal-05802486v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-na",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Transport-based interpolation of dyadic meshes for problems with variable conditions",
  "title_text": "Transport-based interpolation of dyadic meshes for problems with variable conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:58Z",
  "url": "https://research.draconitic.com/paper/8v6qx6hmswjyq",
  "venue": "HAL",
  "versions": []
}