{"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/numerical-generation-of-vector-potentials","title":"Numerical generation of vector potentials from specified magnetic fields","arxiv_id":"1803.10207","date":"2018-03-27","proceeding":null,"authors":["Zachary J. Silberman","Thomas R. Adams","Joshua A. Faber","Zachariah B. Etienne","Ian Ruchlin"],"abstract":"Many codes have been developed to study highly relativistic, magnetized flows around and inside compact objects. Depending on the adopted formalism, some of these codes evolve the vector potential $\\mathbf{A}$, and others evolve the magnetic field $\\mathbf{B}=\\nabla\\times\\mathbf{A}$ directly. Given that these codes possess unique strengths, sometimes it is desirable to start a simulation using a code that evolves $\\mathbf{B}$ and complete it using a code that evolves $\\mathbf{A}$. Thus transferring the data from one code to another would require an inverse curl algorithm. This paper describes two new inverse curl techniques in the context of Cartesian numerical grids: a cell-by-cell method, which scales approximately linearly with the numerical grid, and a global linear algebra approach, which has worse scaling properties but is generally more robust (e.g., in the context of a magnetic field possessing some nonzero divergence). We demonstrate these algorithms successfully generate smooth vector potential configurations in challenging special and general relativistic contexts.","url_abs":"http://arxiv.org/abs/1803.10207v1","url_pdf":"http://arxiv.org/pdf/1803.10207v1.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":"numerical-generation-of-vector-potentials","repo_url":"https://github.com/zsilberman/Inverse-Curl","is_official":1,"mentioned_in_paper":1,"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}