{
  "abstract": "Time-harmonic Maxwell scattering by a perfectly conducting obstacle is governed by the electric field integral equation (EFIE), whose natural energy space is $\\boldsymbol H^{-1/2}(\\mathrm{div}_Γ,Γ)$. For countably parametrized surface deformations, both the operator and its energy space depend on the geometry. We establish operator-valued shape holomorphy of the EFIE operator on a fixed reference space and derive dimension-independent sparse approximation rates. The main analytical difficulty is a fractional mapping property absent from existing $L^2$-based operator-valued shape-holomorphy theory for weakly singular kernels: the Maxwell graph norm requires uniform holomorphy of the complex-deformed scalar single layer as an operator from $H^{-1/2}$ to $H^{1/2}$. We prove this one-order smoothing by realizing the Laplace principal part as the trace of a uniformly sectorial complex-coefficient divergence-form problem on a fixed real ambient domain. Combined with a surface contravariant Piola transformation, which identifies the geometry-dependent Maxwell trace spaces and cancels the surface Jacobians in the pulled-back EFIE exactly, this yields $(\\mathbf b,p,\\varepsilon)$-holomorphy of the EFIE operator family for $\\ell^p$-summable shape deformations, $0<p<1$. Under pointwise exclusion of interior electric resonances, parameter-uniform invertibility is derived rather than assumed, and the surface current and far field inherit the same parametric regularity. Their Legendre coefficients are $\\ell^p$-summable, yielding dimension-independent best $N$-term approximation rates. The operator-level results also transfer to Galerkin boundary element operators on a single reference mesh, with constants independent of the discretization dimension, and provide reusable surrogates for multiple incident fields and bounded linear observables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00466",
  "author_total": 2,
  "authors": [
    {
      "name": "Paul Escapil-Inchauspé"
    },
    {
      "name": "Carlos Jerez-Hanckes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5fzkv7be77c1s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00466",
  "fulltext_url": null,
  "id": "5fzkv7be77c1s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00466",
  "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.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3107|Electromagnetic Scattering and Analysis"
    ]
  ],
  "openalex": "W7206156027",
  "pdf_url": "https://arxiv.org/pdf/2609.00466",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5fzkv7be77c1s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.00466",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00466"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Shape Holomorphy and Sparse Approximation of the Maxwell Electric Field Integral Operator",
  "title_text": "Shape Holomorphy and Sparse Approximation of the Maxwell Electric Field Integral Operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/5fzkv7be77c1s",
  "venue": "arXiv",
  "versions": []
}