Metraipolis › archive › dc_2ee3d612eecf

Transport-Matched Penalties for Diffusion Synthetic Acceleration of Polytopic Discontinuous Galerkin Discretisations — arXiv:2608.28022

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.28022
License (as archived): CC0-1.0
Archived: 2026-10-17T11:22:21.990Z
SHA-256 of the archived text: 5035d094f4fe4003fed9b6f526070716539f336808c55bfdecb32f81cfe3b117
Stable URL of this page: https://metraipolis.com/documento/dc_2ee3d612eecf

How to cite

Transport-Matched Penalties for Diffusion Synthetic Acceleration of Polytopic Discontinuous Galerkin Discretisations — arXiv:2608.28022 — arXiv (en), https://arxiv.org/abs/2608.28022 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2ee3d612eecf (Metraipolis archive dc_2ee3d612eecf, sha256 5035d094f4fe4003fed9b6f526070716539f336808c55bfdecb32f81cfe3b117)

BibTeX

@misc{dc2ee3d612eecf,
  title = {Transport-Matched Penalties for Diffusion Synthetic Acceleration of Polytopic Discontinuous Galerkin Discretisations — arXiv:2608.28022},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.28022},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2ee3d612eecf; sha256 5035d094f4fe4003fed9b6f526070716539f336808c55bfdecb32f81cfe3b117},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.28022. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Diffusion synthetic acceleration is most effective when its diffusion correction reflects the transport discretisation that generates the iteration error. We develop this principle for high-order upwind discontinuous Galerkin discretisations of discrete-ordinates transport on polytopic meshes. From the discrete transport sweep, we derive the exact scalar correction that removes the source-iteration scalar error in one step. We prove that the associated scalar response is positive and self-adjoint, obtain an exact expression for the source-iteration convergence factor, and quantify the additional damping produced by vacuum leakage. Using the exact correction as a reference, we construct a transport-matched modified interior penalty correction whose boundary terms are inherited directly from homogeneous vacuum inflow. In the optically thick regime, the resulting MIP form approximates the exact correction with relative error proportional to the effective cell Knudsen number. This gives a strict acceleration of source iteration, with bounds uniform in mesh size, polynomial degree, and element face count for admissible polytopic meshes. Numerical experiments on Cartesian and centroidal Voronoi meshes confirm the predicted convergence and correction-operator scaling.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-31 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2608.28022 — 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 2026-10-17T11:06:05.067Z dalla pagina https://arxiv.org/catchup/math.NA/2026-08-31?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).