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Frequency-explicit convergence analysis of a multiscale finite element method for highly heterogeneous scattering problems — arXiv:2609.04930

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.04930
License (as archived): CC0-1.0
Archived: 2026-10-16T23:19:16.384Z
SHA-256 of the archived text: 97bbce7d222c8ccbc7ae48ba4a5ae42ee1b4f00c6a12a7235d7f72539b5e200d
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How to cite

Frequency-explicit convergence analysis of a multiscale finite element method for highly heterogeneous scattering problems — arXiv:2609.04930 — arXiv (en), https://arxiv.org/abs/2609.04930 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_859cd6914d91 (Metraipolis archive dc_859cd6914d91, sha256 97bbce7d222c8ccbc7ae48ba4a5ae42ee1b4f00c6a12a7235d7f72539b5e200d)

BibTeX

@misc{dc859cd6914d91,
  title = {Frequency-explicit convergence analysis of a multiscale finite element method for highly heterogeneous scattering problems — arXiv:2609.04930},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.04930},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_859cd6914d91; sha256 97bbce7d222c8ccbc7ae48ba4a5ae42ee1b4f00c6a12a7235d7f72539b5e200d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.04930. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We analyze the numerical approximation of time-harmonic scattering by highly heterogeneous penetrable obstacles. These problems are especially challenging in the high-frequency regime, where the size of the scatterer $L$ is much larger than the wavelength, i.e., the wavenumber $k$ is such that $kL \gg 1$. Here, we further consider the situation where the scatterer contains different materials, with a characteristic size $\varepsilon$ such that $k\varepsilon \ll 1$. We propose a high-order multiscale finite element method, and provide an error analysis that is explicit in both $k$ and $\varepsilon$. Crucially, our error estimates suggest that using a high-order method should reduce the computational cost for large frequencies, which is corroborated by numerical examples.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-07 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA) ; Analysis of PDEs (math.AP).
Pagina del lavoro: https://arxiv.org/abs/2609.04930 — 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 2026-10-16T23:02:57.307Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-07?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).