{
  "abstract": "We consider an inexact version of the Schwarz domain decomposition method in $3$D to solve a Laplace problem in a domain that is the union of two overlapping spheres. We solve each subproblem approximately by projecting its boundary data $L^2$-orthogonally onto the space of spherical harmonics of degree at most $N$. The model problem arises from the ddCOSMO solver used for implicit solvation in computational chemistry. We analyze the Schwarz-spherical domain decomposition method by establishing a new variant of the maximum principle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13793",
  "author_total": 1,
  "authors": [
    {
      "name": "Nibedita Ghosh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a342v1sa2smzf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13793",
  "fulltext_url": null,
  "id": "a342v1sa2smzf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13793",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7221564492",
  "pdf_url": "https://arxiv.org/pdf/2610.13793",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a342v1sa2smzf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13793",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13793"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Analysis of an inexact Schwarz domain decomposition method in 3D",
  "title_text": "Analysis of an inexact Schwarz domain decomposition method in 3D",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/a342v1sa2smzf",
  "venue": "arXiv",
  "versions": []
}