{"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/direction-splitting-of-varphi-functions-in","title":"Direction splitting of $\\varphi$-functions in exponential integrators for $d$-dimensional problems in Kronecker form","arxiv_id":"2304.02327","date":"2023-04-05","proceeding":null,"authors":["Marco Caliari","Fabio Cassini"],"abstract":"In this manuscript, we propose an efficient, practical and easy-to-implement way to approximate actions of $\\varphi$-functions for matrices with $d$-dimensional Kronecker sum structure in the context of exponential integrators up to second order. The method is based on a direction splitting of the involved matrix functions, which lets us exploit the highly efficient level 3 BLAS for the actual computation of the required actions in a $\\mu$-mode fashion. The approach has been successfully tested on two- and three-dimensional problems with various exponential integrators, resulting in a consistent speedup with respect to a technique designed to compute actions of $\\varphi$-functions for Kronecker sums.","url_abs":"https://arxiv.org/abs/2304.02327v1","url_pdf":"https://arxiv.org/pdf/2304.02327v1.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":"direction-splitting-of-varphi-functions-in","repo_url":"https://github.com/caliarim/phisplit","is_official":1,"mentioned_in_paper":1,"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}