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.

翻译：本文提出了一种用于磁准静态涡流问题的高阶等几何公式，该方法基于将场分解为毕奥-萨伐尔驱动的源场和有限元反应场。基于最近提出的仅需表面计算的毕奥-萨伐尔评估方法，我们将简化磁矢势框架推广至准静态区域，并引入了一致的高阶样条离散化方案。所提出的方法避免了线圈网格划分，支持任意绕组路径，并能在简化计算域内实现高阶场近似。数值研究不仅验证了最优收敛速率，还明确了在实践中实现高阶精度所需满足的条件，包括包络界面的几何正则性、精确的核函数积分计算以及源场-反应场耦合中相容的迹空间。