{
  "abstract": "We develop and analyze a three-dimensional pure source transfer domain decomposition method (PSTDDM) for the Helmholtz equation in free space. Extending the two-dimensional PSTDDM proposed by [Du and Wu, J. Sci. Comput., 83(2020),83:68], the proposed method transfers sources successively along the $x_1$, $x_2$, and $x_3$ directions, yielding layer-wise, bar-wise, and block-wise PSTDDMs. The main challenge in the convergence analysis is deriving wavenumber-explicit truncation-error estimates. To address this challenge, we establish inf--sup conditions for the uniaxial perfectly matched layer (UPML) problem under relaxed restrictions on the PML parameters and reformulate the source-transfer operators. We then introduce a positive-definite reconstruction step that produces a globally conforming approximation. In addition, a new quantitative lower bound is established for the imaginary part of the complex PML distance, more easily yielding exponential decay estimates in three dimensions. These lead to wavenumber-explicit convergence estimates for all three PSTDDMs. Numerical experiments demonstrate the effectiveness of the proposed methods both as direct solvers and as preconditioners for GMRES.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19435",
  "author_total": 3,
  "authors": [
    {
      "name": "Xinran Bai"
    },
    {
      "name": "Yu Du"
    },
    {
      "name": "Haijun Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jq9z4c4wxww3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19435",
  "fulltext_url": null,
  "id": "3jq9z4c4wxww3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19435",
  "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": "W7222192752",
  "pdf_url": "https://arxiv.org/pdf/2610.19435",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jq9z4c4wxww3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19435",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19435"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A pure source transfer domain decomposition method for Helmholtz equations in 3D unbounded domain",
  "title_text": "A pure source transfer domain decomposition method for Helmholtz equations in 3D unbounded domain",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/3jq9z4c4wxww3",
  "venue": "arXiv",
  "versions": []
}