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A pure source transfer domain decomposition method for Helmholtz equations in 3D unbounded domain — arXiv:2610.19435

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.19435
License (as archived): CC0-1.0
Archived: 2026-10-15T21:52:26.627Z
SHA-256 of the archived text: 03ce001d0d24e122a92689d357571802716e370864ca1af3f7324db0bbe350d2
Stable URL of this page: https://metraipolis.com/documento/dc_255cd57bb274

How to cite

A pure source transfer domain decomposition method for Helmholtz equations in 3D unbounded domain — arXiv:2610.19435 — arXiv (en), https://arxiv.org/abs/2610.19435 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_255cd57bb274 (Metraipolis archive dc_255cd57bb274, sha256 03ce001d0d24e122a92689d357571802716e370864ca1af3f7324db0bbe350d2)

BibTeX

@misc{dc255cd57bb274,
  title = {A pure source transfer domain decomposition method for Helmholtz equations in 3D unbounded domain — arXiv:2610.19435},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.19435},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_255cd57bb274; sha256 03ce001d0d24e122a92689d357571802716e370864ca1af3f7324db0bbe350d2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.19435. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We develop and analyze a three-dimensional pure source transfer domain decomposition method (PSTDDM) for the Helmholtz equation in free space. Extending the two-dimensional PSTDDM proposed by [Du and Wu, J. Sci. Comput., 83(2020),83:68], the proposed method transfers sources successively along the $x_1$, $x_2$, and $x_3$ directions, yielding layer-wise, bar-wise, and block-wise PSTDDMs. The main challenge in the convergence analysis is deriving wavenumber-explicit truncation-error estimates. To address this challenge, we establish inf--sup conditions for the uniaxial perfectly matched layer (UPML) problem under relaxed restrictions on the PML parameters and reformulate the source-transfer operators. We then introduce a positive-definite reconstruction step that produces a globally conforming approximation. In addition, a new quantitative lower bound is established for the imaginary part of the complex PML distance, more easily yielding exponential decay estimates in three dimensions. These lead to wavenumber-explicit convergence estimates for all three PSTDDMs. Numerical experiments demonstrate the effectiveness of the proposed methods both as direct solvers and as preconditioners for GMRES.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.NA, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2610.19435 — 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 2026-10-15T21:36:59.406Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).