A Reduced Magnetic Vector Potential Approach with Higher-Order Splines
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910034051465216 |
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| author | Backmeyer, Merle D'Angelo, Laura A. M. Ramdane, Brahim Schöps, Sebastian |
| author_facet | Backmeyer, Merle D'Angelo, Laura A. M. Ramdane, Brahim Schöps, Sebastian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22997 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Reduced Magnetic Vector Potential Approach with Higher-Order Splines Backmeyer, Merle D'Angelo, Laura A. M. Ramdane, Brahim Schöps, Sebastian Numerical Analysis Computational Engineering, Finance, and Science 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. |
| title | A Reduced Magnetic Vector Potential Approach with Higher-Order Splines |
| topic | Numerical Analysis Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2602.22997 |