一种基于高阶样条的简化磁矢势方法
A Reduced Magnetic Vector Potential Approach with Higher-Order Splines
AI总结：
本文提出了一种基于高阶样条的简化磁矢势方法，用于解决磁流体静力学涡流问题，实现了高阶精度的场近似。
摘要：
本文提出了一种高阶等参数格式，用于磁流体静力学涡流问题，该方法基于将Biot-Savart驱动源场和有限元反应场分解开来。在基于最近提出的仅表面Biot-Savart评估的基础上，我们扩展了简化磁矢势框架到准静态领域，并引入了一种一致的高阶样条离散化方法。所得到的方法避免了线圈网格划分，支持任意缠绕路径，并在减少的计算域内实现了高阶场近似。除了建立最优收敛率外，数值研究还确定了在实践中恢复高阶精度所需的要求，包括包围界面的几何正则性、准确的核二次积分以及源-反应耦合的兼容迹空间。
英文摘要：
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.
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