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A hybrid TT/QTT discontinuous Galerkin method with fixed-matrix upwinding for three-dimensional transient multigroup neutron transport — arXiv:2611.04360

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.04360
License (as archived): CC0-1.0
Archived: 2026-11-04T19:00:07.358Z
SHA-256 of the archived text: 0cb8fdf6a265ce28c1b6dedea7825c3504c5731149b96f6908179b51387b58ce
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How to cite

A hybrid TT/QTT discontinuous Galerkin method with fixed-matrix upwinding for three-dimensional transient multigroup neutron transport — arXiv:2611.04360 — arXiv (en), https://arxiv.org/abs/2611.04360 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_da2968e95d64 (Metraipolis archive dc_da2968e95d64, sha256 0cb8fdf6a265ce28c1b6dedea7825c3504c5731149b96f6908179b51387b58ce)

BibTeX

@misc{dcda2968e95d64,
  title = {A hybrid TT/QTT discontinuous Galerkin method with fixed-matrix upwinding for three-dimensional transient multigroup neutron transport — arXiv:2611.04360},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.04360},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_da2968e95d64; sha256 0cb8fdf6a265ce28c1b6dedea7825c3504c5731149b96f6908179b51387b58ce},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.04360. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We develop a hybrid tensor-train/quantized tensor-train (TT/QTT) upwind discontinuous Galerkin method for three-dimensional transient multigroup neutron transport. The central contribution is a fixed-matrix upwind construction: two spatial DG matrices serve all directions and energy groups, with signed and absolute direction-cosine factors preserving Kronecker structure. For homogeneous materials on uniform Cartesian grids, operator rank bounds are independent of mesh size, group count and direction count at fixed scattering order. We derive a conditional global step-defect bound and enforce group-integrated balance of the compressed system. Crank-Nicolson tests show second-order convergence on a separable manufactured solution whose finest final state occupies 13 kB instead of 35 TB, a compression factor of $2.7\times10^9$. A modified rank-adaptive basis-update and Galerkin integrator (TT-BUG) advances passive and active bursts with approximately half a billion unknowns. Selected runs are 15-20 times faster than AMEn at comparable verified scalar-flux errors. In the reported anisotropic active-burst configurations, TT-BUG takes 14.3 s on one processor versus 716 s for OpenSn on 24 processors: approximately 50 times less wall time and 1200 times less allocated processor-time cost. This compares reported configurations rather than matched physical errors. OpenSn provides an independent discretization check. The modified TT-BUG source-onset and saturation treatment is tested numerically; its order, convergence and general tolerance-to-error relation remain unproved.

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/2611.04360 — 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 2026-11-04T18:38:07.295Z dalla pagina https://arxiv.org/list/math.NA/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).