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Embedding a de Rham Complex Structure into Eig-PIELM for Maxwell Eigenvalue Problems — arXiv:2611.02337

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02337
License (as archived): CC0-1.0
Archived: 2026-11-03T18:40:42.583Z
SHA-256 of the archived text: 28d3251ec47d213cbfb030bff2172d3566a6f4b358dc59305be2bf170ffb1b8a
Stable URL of this page: https://metraipolis.com/documento/dc_7c869d05efca

How to cite

Embedding a de Rham Complex Structure into Eig-PIELM for Maxwell Eigenvalue Problems — arXiv:2611.02337 — arXiv (en), https://arxiv.org/abs/2611.02337 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7c869d05efca (Metraipolis archive dc_7c869d05efca, sha256 28d3251ec47d213cbfb030bff2172d3566a6f4b358dc59305be2bf170ffb1b8a)

BibTeX

@misc{dc7c869d05efca,
  title = {Embedding a de Rham Complex Structure into Eig-PIELM for Maxwell Eigenvalue Problems — arXiv:2611.02337},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02337},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7c869d05efca; sha256 28d3251ec47d213cbfb030bff2172d3566a6f4b358dc59305be2bf170ffb1b8a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02337. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The perfect electric conductor (PEC) boundary condition alone does not eliminate the gradient nullspace of the Maxwell curl-curl operator. Consequently, a boundary-only Maxwell implementation of Eig-PIELM, an eigenvalue extension of the physics-informed extreme learning machine (PIELM), may retain represented gradient modes in its reduced trial space, producing nonphysical, gradient-contaminated modes. We develop dR-Eig-PIELM, a finite-dimensional structure-preserving extension that retains the linear-coefficient, boundary-null-space, and one-shot multimode architecture of Eig-PIELM. It combines compatible tensor-product grad--curl trial spaces with a constrained null-space construction to restrict the sampled PEC space to the mass-orthogonal complement of the represented gradient image before the eigensolve. Symmetric weak-form Gram assembly yields a symmetric-definite reduced eigenproblem without an eigenvalue cutoff under the stated sampling and material-positivity assumptions. For rectangles and cuboids, we establish fixed-degree exactness at the PEC vector-field space and derive rank and dimension identities. Numerical experiments show that dR-Eig-PIELM excludes the spurious eigenmodes with significant gradient components observed in the boundary-only baseline. The method exhibits rapid convergence with increasing polynomial degree and competitive work--precision performance in the tested configurations. A covariantly mapped waveguide example illustrates the potential of dR-Eig-PIELM for integration into design optimization workflows through a constrained local geometry update driven by computed cutoff frequencies and their sensitivities. This work provides a mathematical and computational framework for separating represented gradient modes from physical Maxwell eigenmodes within Eig-PIELM and supports its use in waveguide spectral analysis and geometry design.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2611.02337 — 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 2026-11-03T18:12:54.765Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).