{
  "abstract": "We develop a unified theory of vectorial quasi-interpolation that exactly preserves intrinsic physical structures characterized by systems of linear constant-coefficient differential operators, including divergence-free and curl-free constraints as special cases. The key ingredient is a family of matrix-valued kernels constructed from an orthogonal projector in the frequency domain, whose columns analytically satisfy the prescribed constraints. The resulting quasi-interpolant is a weighted combination of kernel translates with sampled function values as coefficients, and therefore requires no constrained optimization. Simultaneous error estimates for the approximand and its derivatives are established within a bias-variance framework. For numerical vector-field decomposition, we introduce a generalized Helmholtz--Hodge decomposition that splits a smooth vector field into two components with distinct physical structures, and develop corresponding structure-preserving quasi-interpolation schemes and error estimates. Explicit kernels are derived for several representative constraints, including steady-state acoustic constraints, combined divergence-curl constraints, coupled divergence-free constraints, and second-order Saint-Venant compatibility conditions. Numerical experiments confirm the theoretical error estimates and exact structure preservation, demonstrate accurate identification of sources and sinks, and show three-dimensional reconstruction of generalized Helmholtz--Hodge components for general smooth vector fields without prior constraint assumptions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12912",
  "author_total": 1,
  "authors": [
    {
      "name": "Wenwu Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bxxwp900cww09.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12912",
  "fulltext_url": null,
  "id": "bxxwp900cww09",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12912",
  "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",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7212998226",
  "pdf_url": "https://arxiv.org/pdf/2609.12912",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxxwp900cww09.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12912",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12912"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Structure-preserving quasi-interpolation for vector-valued function with multiple physical constraints",
  "title_text": "Structure-preserving quasi-interpolation for vector-valued function with multiple physical constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/bxxwp900cww09",
  "venue": "arXiv",
  "versions": []
}