{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/exploring-one-cell-inversion-method-for","title":"Exploring One-Cell Inversion Method for Transient Transport on GPU","arxiv_id":"2305.13555","date":"2023-05-22","proceeding":null,"authors":["J. P. Morgan","Ilham Variansyah","Todd S. Palmer","Kyle E. Niemeyer"],"abstract":"To find deterministic solutions to the transient $S_N$ neutron transport equation, iterative schemes are typically used to treat the scattering (and fission) source terms. We explore the one-cell inversion iteration scheme to do this on the GPU and make comparisons to a source iteration scheme. We examine convergence behavior, through the analysis of spectral radii, of both one-cell inversion and source iterations. To further boost the GPU parallel efficiency, we derive a higher-order discretization method, simple corner balance (in space) and multiple balance (in time), to add more work to the threads and gain accuracy. Fourier analysis on this higher-order numerical method shows that it is unconditionally stable, but it can produce negative flux alterations that are critically damped through time. We explore a whole-problem (in all angle and all cell) sparse linear algebra framework, for both iterative schemes, to quickly produce performant code for GPUs. Despite one-cell inversion requiring additional iterations to convergence, those iterations can be done faster to provide a significant speedup over source iteration in quadrature sets at or below $S_{128}$. Going forward we will produce a two-dimensional implementation of this code to experiment with memory and performance impacts of a whole-problem framework including methods of synthetic acceleration and pre-conditioners for this scheme, then we will begin making direct comparisons to traditionally implemented source iteration in production code.","url_abs":"https://arxiv.org/abs/2305.13555v2","url_pdf":"https://arxiv.org/pdf/2305.13555v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"exploring-one-cell-inversion-method-for","repo_url":"https://github.com/CEMeNT-PSAAP/Therefore","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}