This article presents a boundary element method (BEM) formulation coupled with high-order surface impedance boundary conditions (SIBCs) for axisymmetric eddy current problems. The formulation is based on the perturbation theory (PT) and the reduced magnetic scalar potential. A big advantage of the proposed approach is that if the solution is sought at different frequencies, the boundary integral equations can be solved only once and, then, the fields are easily computed at any frequency using a series expansion according to PT. Three test problems are solved, for which the reference solution is given by the standard finite-element method (FEM). The convergence of BEM-SIBC results toward FEM solution with respect to frequency is verified. The proposed approach requires reduced memory and computational times compared to the standard FEM and can be applied with linear, isotropic, and homogeneous materials.

中文翻译：

---

边界元公式强制轴对称涡流问题的高阶表面阻抗边界条件


本文提出了一种与高阶表面阻抗边界条件 (SIBC) 相结合的边界元法 (BEM) 公式，用于解决轴对称涡流问题。该公式基于微扰理论 (PT) 和简化的磁标量势。该方法的一大优点是，如果在不同频率下寻求解，则边界积分方程只需求解一次，然后，使用根据 PT 的级数展开可以轻松计算任何频率下的场。解决了三个测试问题，并通过标准有限元法（FEM）给出了参考解。验证了 BEM-SIBC 结果对于频率方面的 FEM 解的收敛性。与标准有限元法相比，所提出的方法需要减少内存和计算时间，并且可以应用于线性、各向同性和均质材料。