{
  "abstract": "We develop a numerical framework for three-dimensional quasiperiodic Maxwell eigenvalue problems obtained through a six-dimensional periodic embedding. A projected Bloch--Fourier discretization yields a structured generalized eigenvalue problem with a large gradient-type kernel. Explicit orthonormal bases for the longitudinal and transverse subspaces remove this kernel exactly and reduce the original generalized eigenvalue problem to a null-space-free standard eigenvalue problem containing only the positive spectrum. An explicit inverse representation of the reduced operator avoids nested inner--outer linear solves and leads to an inverse Lanczos method whose main inner computation is a Hermitian positive definite conjugate-gradient solve with condition number bounded by that of the mass matrix; a residual estimate quantifies the effect of inner solves on the inverse Ritz pairs. To recover the computed modes in physical space, the six-dimensional Fourier eigenvectors are reconstructed on a three-dimensional Yee grid by a separated multi-center Taylor expansion, which avoids the dense Fourier-to-grid phase matrix and remains practical when direct dense reconstruction becomes prohibitively expensive. Local weighted Rayleigh quotients provide an independent physical-space validation, and their mass-weighted expectation is proved to equal the cropped Yee Rayleigh quotient under a partition-of-unity condition. Numerical experiments confirm the accuracy and computational effectiveness of the proposed framework and its physical-space recovery of three-dimensional quasiperiodic Maxwell modes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06965",
  "author_total": 4,
  "authors": [
    {
      "name": "Teng-Chao Sun"
    },
    {
      "name": "Tiexiang Li"
    },
    {
      "name": "Wen-Wei Lin"
    },
    {
      "name": "Xing-Long Lyu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ef3v5cb9bp1en.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06965",
  "fulltext_url": null,
  "id": "ef3v5cb9bp1en",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06965",
  "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",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7212046863",
  "pdf_url": "https://arxiv.org/pdf/2609.06965",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ef3v5cb9bp1en.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.06965",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06965"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Null-Space-Free 6D Spectral Embedding with Local Rayleigh Quotient Recovery for 3D Quasiperiodic Maxwell's Eigenproblems",
  "title_text": "Null-Space-Free 6D Spectral Embedding with Local Rayleigh Quotient Recovery for 3D Quasiperiodic Maxwell's Eigenproblems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/ef3v5cb9bp1en",
  "venue": "arXiv",
  "versions": []
}