{
  "abstract": "We introduce an r-adaptive (or r-refinement) multi-patch isogeometric method that applies to parametric curves or surfaces embedded in two or three dimensions as well as to volumetric domains. The proposed approach preserves C 0 continuity across patch interfaces. Moreover, if the underlying geometric parameterization is G 1 -compatible, then the resulting moving mesh mapping also preserves G 1 regularity across the interfaces. The global adaptive mesh is constructed by iteratively solving a Laplace equation in the computational domain, through a fast diagonalization solver that exploits the Kronecker-product structure of the matrices. Mesh adaptation is driven by a moving-mesh partial differential equation with a density function derived from either an arc-length monitor or a posteriori error indicator. Numerical experiments are carried out using an analytic density function, with additional applications to singular solutions and to the highly anisotropic diffusion equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Mustapha Bahari"
    },
    {
      "name": "Blaise Faugeras"
    },
    {
      "name": "Bernard Mourrain"
    },
    {
      "name": "Francesca Rapetti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4v5aptgtgmh53.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "4v5aptgtgmh53",
  "issns": [],
  "landing_url": "https://hal.science/hal-05761930v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-na"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05761930/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4v5aptgtgmh53.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "hal-05761930",
      "source": "hal",
      "url": "https://hal.science/hal-05761930v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-na",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Efficient r-Adaptive Multipatch Isogeometric Method in Arbitrary Dimension",
  "title_text": "Efficient r-Adaptive Multipatch Isogeometric Method in Arbitrary Dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:40Z",
  "url": "https://research.draconitic.com/paper/4v5aptgtgmh53",
  "venue": "HAL",
  "versions": []
}