{
  "abstract": "We consider boundary integral methods for Stokes mobility and resistance problems involving smooth axisymmetric particles. A primary numerical challenge is the accurate and efficient evaluation of layer potentials at off-surface points close to particle surfaces. We present a tolerance-driven workflow for evaluating the Stokes double layer potential at such evaluation points (targets) to prescribed accuracy while avoiding unnecessary computational cost. For each target--particle interaction, a fast classifier selects the least costly option estimated to meet the tolerance among standard, upsampled, and special quadrature. Geometry-dependent unit-density error indicators are precomputed and tabulated in reduced cylindrical coordinates, then combined on the fly with a local layer-density modifier, making its cost negligible relative to evaluating the potential. Targets requiring special quadrature are treated using a stabilized version of singularity swap surface quadrature: the periodic azimuthal integral is evaluated first using translated singularity swap quadrature to prevent severe cancellation near the surface, followed by adaptive Gauss--Legendre quadrature in the polar direction guided by error indicators. We integrate this workflow into a boundary integral solver with precomputed quadrature by expansion for on-surface self-interactions and demonstrate the workflow's performance for challenging configurations of spheroidal particles. Numerical results show that target classification is highly accurate. The prescribed tolerance is met for nearly all target--particle interactions and the error remains within a modest factor of the tolerance in the few remaining cases. Although the experiments focus on the Stokes double layer potential for spheroids, the off-surface framework applies to general smooth axisymmetric surfaces and can be easily adapted to other Stokes layer potentials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11778",
  "author_total": 3,
  "authors": [
    {
      "name": "David Krantz"
    },
    {
      "name": "Pritpal Matharu"
    },
    {
      "name": "Anna-Karin Tornberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cmp3pjr8v5dbz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11778",
  "fulltext_url": null,
  "id": "cmp3pjr8v5dbz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11778",
  "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",
      "3107|Electromagnetic Scattering and Analysis"
    ]
  ],
  "openalex": "W7212240419",
  "pdf_url": "https://arxiv.org/pdf/2609.11778",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cmp3pjr8v5dbz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11778",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11778"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Tolerance-driven close evaluation of the Stokes double layer potential on axisymmetric surfaces",
  "title_text": "Tolerance-driven close evaluation of the Stokes double layer potential on axisymmetric surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/cmp3pjr8v5dbz",
  "venue": "arXiv",
  "versions": []
}