Metraipolis › archive › dc_136bbfc81868

Null-Space-Free 6D Spectral Embedding with Local Rayleigh Quotient Recovery for 3D Quasiperiodic Maxwell's Eigenproblems — arXiv:2609.06965

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.06965
License (as archived): CC0-1.0
Archived: 2026-10-16T14:48:00.982Z
SHA-256 of the archived text: f7722d2b90ada2afd8c39a083b4502fd4aac9417a2a476995bf0cdcc015e76f6
Stable URL of this page: https://metraipolis.com/documento/dc_136bbfc81868

How to cite

Null-Space-Free 6D Spectral Embedding with Local Rayleigh Quotient Recovery for 3D Quasiperiodic Maxwell's Eigenproblems — arXiv:2609.06965 — arXiv (en), https://arxiv.org/abs/2609.06965 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_136bbfc81868 (Metraipolis archive dc_136bbfc81868, sha256 f7722d2b90ada2afd8c39a083b4502fd4aac9417a2a476995bf0cdcc015e76f6)

BibTeX

@misc{dc136bbfc81868,
  title = {Null-Space-Free 6D Spectral Embedding with Local Rayleigh Quotient Recovery for 3D Quasiperiodic Maxwell's Eigenproblems — arXiv:2609.06965},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.06965},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_136bbfc81868; sha256 f7722d2b90ada2afd8c39a083b4502fd4aac9417a2a476995bf0cdcc015e76f6},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.06965. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.06965 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T14:30:08.707Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).