A space-time hybrid parareal method for kinetic equations in the diffusive scaling

[2511.13386] A space-time hybrid parareal method for kinetic equations in the diffusive scaling Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:2511.13386 (math) [Submitted on 17 Nov 2025 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: A space-time hybrid parareal method for kinetic equations in the diffusive scaling Authors: Tino Laidin View PDF HTML (experimental) Abstract: We present a novel multiscale numerical approach that combines parallel-in-time computation with hybrid domain adaptation for linear collisional kinetic equations in the diffusive regime. The method addresses the computational challenges of kinetic simulations by integrating two complementary strategies: a parareal temporal parallelization method and a dynamic spatial domain adaptation based on perturbative analysis. The multiscale parallel-in-time approach introduced in \cite{LaidinRey2025} is here considered in the diffusive scaling. It employs a coarse fluid solver for efficient temporal propagation coupled with a fine, spatially-hybridized, kinetic solver for accurate resolution. Domain adaptation is governed by two criteria: one measuring the deviation from local velocity equilibrium, and another based on macroscopic quantities available throughout the computational domain. An asymptotic preserving micro-macro decomposition framework handles the stiffness of the original problem. This fully hybrid methodology significantly reduces computational costs compared to full kinetic approaches by exploiting the lower dimensionality of asymptotic fluid models while maintaining accuracy through selective kinetic resolution. The method demonstrates substantial speedup capabilities and efficiency gains across various kinetic regimes. Comments: 16 pages, 8 figures, 3 tables Subjects: Numerical Analysis (math.NA) MSC classes: 35Q20, 65M22, 82C40, 65M55, 65Y05 Cite as: arXiv:2511.13386 [math.NA] (or arXiv:2511.13386v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2511.13386 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tino Laidin [ view email ] [v1] Mon, 17 Nov 2025 13:58:07 UTC (1,557 KB) [v2] Tue, 25 Aug 2026 08:51:46 UTC (1,559 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2025-11 Change to browse by: cs cs.NA math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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