{
  "abstract": "We analyze the numerical approximation of time-harmonic scattering by highly heterogeneous penetrable obstacles. These problems are especially challenging in the high-frequency regime, where the size of the scatterer ℓD is much larger than the wavelength, i.e., the wavenumber k is such that kℓD ≫ 1. Here, we further consider the situation where the scatterer contains different materials, with a characteristic size ε such that kε ≪ 1. We propose a high-order multiscale finite element method, and provide an error analysis that is explicit in both k and ε. Crucially, our error estimates suggest that using a high-order method should reduce the computational cost for large frequencies, which is corroborated by numerical examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04930",
  "author_total": 2,
  "authors": [
    {
      "name": "Théophile Chaumont-Frelet"
    },
    {
      "name": "zakaria kassali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ch143mw1d0a3k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04930",
  "fulltext_url": null,
  "id": "ch143mw1d0a3k",
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  "landing_url": "https://inria.hal.science/hal-05738526v1",
  "language": "en",
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  "licence_label": "CC BY-NC-ND 4.0",
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  "metadata_licence": "CC0-1.0",
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      "1703|Advanced Mathematical Modeling in Engineering"
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  "openalex": "W7210893762",
  "pdf_url": "https://inria.hal.science/hal-05738526/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ch143mw1d0a3k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:29Z",
      "native_id": "hal-05738526",
      "source": "hal",
      "url": "https://inria.hal.science/hal-05738526v1"
    },
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04930",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04930"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Frequency-explicit convergence analysis of a multiscale finite element method for highly heterogeneous scattering problems",
  "title_text": "Frequency-explicit convergence analysis of a multiscale finite element method for highly heterogeneous scattering problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/ch143mw1d0a3k",
  "venue": "HAL",
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}