{
  "abstract": "We present a boundary integral method for evaluating electron repulsion integrals (ERIs) in dielectric environments of piecewise constant permittivity. This generalizes conventional bare-Coulomb ERIs by incorporating screening from structured dielectric surroundings, such as the substrates and/or encapsulating layers present in modern two-dimensional-material devices. We formulate the problem as a second-kind boundary integral equation for the induced surface charge on the dielectric interfaces, and discretize it with a Nyström method on adaptively refined panels. The incident potential generated by each smooth orbital source density is evaluated by a Fourier truncated-kernel method in or near to its source box, and by fast multipole method (FMM) accelerated quadrature farther away. The linear system is solved by a Krylov iteration also accelerated by the FMM. We focus on cuboidal device geometries, and retain efficiency at high aspect ratios via close-to-touching panel quadratures. We further develop a distributed pipeline that computes the full ERI tensor, comprising thousands of orbital pairs, embedded in a single dielectric geometry. We demonstrate the method on an effective three-layer graphene slab over a Si/SiO$_2$ heterojunction, focusing on the central graphene layer represented by $198$ $p_z$-like orbitals, retaining the $2613^2$ non-negligible entries of the $198^4$-sized ERI tensor. The model is resolved on $1.3$ million surface unknowns, achieving a relative error of $0.004\\%$, at a cost of $22$ node-hours.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26745",
  "author_total": 4,
  "authors": [
    {
      "name": "Xuanzhao Gao"
    },
    {
      "name": "Malte Rösner"
    },
    {
      "name": "Jason Kaye"
    },
    {
      "name": "Alex Barnett"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9mwbmgxk0c5hm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26745",
  "fulltext_url": null,
  "id": "9mwbmgxk0c5hm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26745",
  "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",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3107|Electromagnetic Scattering and Analysis"
    ]
  ],
  "openalex": "W7222999432",
  "pdf_url": "https://arxiv.org/pdf/2610.26745",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9mwbmgxk0c5hm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.26745",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26745"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "A boundary integral method for computing electron repulsion integrals in heterogeneous dielectric environments",
  "title_text": "A boundary integral method for computing electron repulsion integrals in heterogeneous dielectric environments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/9mwbmgxk0c5hm",
  "venue": "arXiv",
  "versions": []
}