{
  "abstract": "A symmetry-inheritance and exact domain-reduction framework is developed for the second-order vector wave equation of the electric field in bounded domains with a perfect electric conductor (PEC) boundary and general spatially varying anisotropic media. Orthogonal group actions on polar vectors, axial vectors, and second-order constitutive tensors are used to derive the transformed curl--curl equation and PEC trace directly from the original boundary-value problem. Under unique solvability, the common symmetry group of the problem data is inherited by the electric field. When the symmetry group of the electromagnetic medium admits a mirror symmetry, an arbitrary impressed current can be decomposed by the associated reflection projectors into mirror-even and mirror-odd components. The corresponding full-domain fields inherit the respective parities, and their exact restriction to one half-domain yields a perfect magnetic conductor (PMC) condition for the even field and a PEC condition for the odd field. The original problem is therefore represented exactly by two independent reduced-domain problems. A symmetry-compatible first-family Nédélec discretization preserves this decomposition at the discrete level. Analytical and numerical results verify the symmetry-inheritance theory, the exact PEC/PMC reduced-domain formulations, and the discrete reconstruction for constant and spatially varying anisotropic conductive media under both symmetric and asymmetric excitations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29481",
  "author_total": 1,
  "authors": [
    {
      "name": "Wei Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cysm3nanvfwzj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29481",
  "fulltext_url": null,
  "id": "cysm3nanvfwzj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29481",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "3107|Electromagnetic Scattering and Analysis"
    ]
  ],
  "openalex": "W7223202379",
  "pdf_url": "https://arxiv.org/pdf/2610.29481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cysm3nanvfwzj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Symmetry Inheritance and Exact Mirror Symmetry Reduction for Electric Field Vector Wave Problems with PEC Boundaries",
  "title_text": "Symmetry Inheritance and Exact Mirror Symmetry Reduction for Electric Field Vector Wave Problems with PEC Boundaries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/cysm3nanvfwzj",
  "venue": "arXiv",
  "versions": []
}