{
  "abstract": "We develop an adaptive localized orthogonal decomposition (ALOD) method for Helmholtz problems with parametrized loads. Under standard resolution, oversampling, and discrete-stability conditions, we establish, to our knowledge, the first wavenumber-robust residual a posteriori error estimate for a Helmholtz LOD discretization. The estimate is two-sided relative to the fine-grid solution and includes a computable bound for the corrector-localization error. In addition, we design a novel family-aware adaptive algorithm using additive Schwarz corrections to construct a shared regional enrichment space for Helmholtz problems with multiple loads. Energy-weighted proper orthogonal decomposition compresses this space. We establish stability and quasi-optimality of the enriched formulation, with bounds independent of the enrichment space. Numerical experiments demonstrate the effectiveness of ALOD for multiple loads and large wavenumbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24776",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuwen Li"
    },
    {
      "name": "Chuxin Que"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/es1992xg76nfz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24776",
  "fulltext_url": null,
  "id": "es1992xg76nfz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24776",
  "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",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7214007955",
  "pdf_url": "https://arxiv.org/pdf/2609.24776",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/es1992xg76nfz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2609.24776",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24776"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "An adaptive localized orthogonal decomposition method for Helmholtz problems",
  "title_text": "An adaptive localized orthogonal decomposition method for Helmholtz problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/es1992xg76nfz",
  "venue": "arXiv",
  "versions": []
}