A Reduced Magnetic Vector Potential Approach with Higher-Order Splines

[2602.22997] A Reduced Magnetic Vector Potential Approach with Higher-Order Splines Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:2602.22997 (math) [Submitted on 26 Feb 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: A Reduced Magnetic Vector Potential Approach with Higher-Order Splines Authors: Merle Backmeyer , Laura A. M. D'Angelo , Brahim Ramdane , Sebastian Schöps View PDF HTML (experimental) Abstract: This work presents a high-order isogeometric formulation for magnetoquasistatic eddy-current problems based on a decomposition into Biot-Savart-driven source fields and finite-element reaction fields. Building upon a recently proposed surface-only Biot-Savart evaluation, we generalize the reduced magnetic vector potential framework to the quasistatic regime and introduce a consistent high-order spline discretization. The resulting method avoids coil meshing, supports arbitrary winding paths, and enables high-order field approximation within a reduced computational domain. Beyond establishing optimal convergence rates, the numerical investigation identifies the requirements necessary to recover high-order accuracy in practice, including geometric regularity of the enclosing interface, accurate kernel quadrature, and compatible trace spaces for the source-reaction coupling. Comments: 7 pages, 6 figures Subjects: Numerical Analysis (math.NA) ; Computational Engineering, Finance, and Science (cs.CE) Cite as: arXiv:2602.22997 [math.NA] (or arXiv:2602.22997v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2602.22997 Focus to learn more arXiv-issued DOI via DataCite Journal reference: IEEE Transaction on Magnetics, 2026 Related DOI : https://doi.org/10.1109/TMAG.2026.3716008 Focus to learn more DOI(s) linking to related resources Submission history From: Merle Backmeyer [ view email ] [v1] Thu, 26 Feb 2026 13:39:00 UTC (104 KB) [v2] Fri, 28 Aug 2026 10:13:28 UTC (160 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-02 Change to browse by: cs cs.CE 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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