{"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/asymptotic-preserving-and-energy-stable-1","title":"Asymptotic-preserving and energy stable dynamical low-rank approximation for thermal radiative transfer equations","arxiv_id":"2402.16746","date":"2024-02-26","proceeding":null,"authors":["Chinmay Patwardhan","Martin Frank","Jonas Kusch"],"abstract":"The thermal radiative transfer equations model temperature evolution through a background medium as a result of radiation. When a large number of particles are absorbed in a short time scale, the dynamics tend to a non-linear diffusion-type equation called the Rosseland approximation. The main challenges for constructing numerical schemes that exhibit the correct limiting behavior are posed by the solution's high-dimensional phase space and multi-scale effects. In this work, we propose an asymptotic-preserving and rank-adaptive dynamical low-rank approximation scheme based on the macro-micro decomposition of the particle density and a modified augmented basis-update \\& Galerkin integrator. We show that this scheme, for linear particle emission by the material, dissipates energy over time under a step size restriction that captures the hyperbolic and parabolic CFL conditions. We demonstrate the efficacy of the proposed method in a series of numerical experiments.","url_abs":"https://arxiv.org/abs/2402.16746v1","url_pdf":"https://arxiv.org/pdf/2402.16746v1.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":"asymptotic-preserving-and-energy-stable-1","repo_url":"https://github.com/chinsp/publication-Low-rank-for-uncertain-radiative-transfer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}