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Isogeometric analysis for the Helmholtz transmission eigenvalue problem — arXiv:2609.21862

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.21862
License (as archived): CC0-1.0
Archived: 2026-10-10T02:10:08.751Z
SHA-256 of the archived text: ef38350efe3a359eda88f8e88e832fba57df403408c788046e5004309b577f76
Stable URL of this page: https://metraipolis.com/documento/dc_fa150346f76d

How to cite

Isogeometric analysis for the Helmholtz transmission eigenvalue problem — arXiv:2609.21862 — arXiv (en), https://arxiv.org/abs/2609.21862 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fa150346f76d (Metraipolis archive dc_fa150346f76d, sha256 ef38350efe3a359eda88f8e88e832fba57df403408c788046e5004309b577f76)

BibTeX

@misc{dcfa150346f76d,
  title = {Isogeometric analysis for the Helmholtz transmission eigenvalue problem — arXiv:2609.21862},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.21862},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fa150346f76d; sha256 ef38350efe3a359eda88f8e88e832fba57df403408c788046e5004309b577f76},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.21862. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The transmission eigenvalue problem plays an increasingly important role in inverse scattering theory. Although significant progress has been made in developing efficient numerical methods for the problem over the last two decades, its numerical treatment for curved domains in $\mathbb{R}^d$ ($d=2,3$) remains challenging. In this paper, we introduce and analyze a geometrically flexible and $H^2$-conforming isogeometric method for solving a fourth-order, quadratic and non-self-adjoint eigenvalue problem arising from the Helmholtz transmission eigenvalue problem. Using the spectral approximation theory for compact non-self-adjoint operators, we derive optimal error estimates for the discrete eigenvalues and eigenfunctions. Numerical results for the two- and three-dimensional benchmark problems, including those defined in curved domains, are presented to verify our theoretical results, and to demonstrate the advantages of the method over existing numerical methods in terms of both accuracy and geometric flexibility.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-21 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.21862 — 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 2026-10-10T01:48:04.989Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).