The problem under consideration is that of time-harmonic eddy current problems in linear ferromagnetic materials surrounded by a dielectric medium with a smooth common interface. Assuming axisymmetric geometries and orthoradial axisymmetric data, we construct an efficient multiscale expansion for the orthoradial solution that provides reduced computational costs. We investigate numerically the accuracy of the approach using an analytical procedure and infinite cylinders as well. It results that the computation of two asymptotics is sufficient to ensure accurate solutions in the case of low frequencies.

翻译：本文考虑线性铁磁材料中时谐涡流问题，该材料被介电介质包围且两者具有光滑公共界面。在轴对称几何与正交径向轴对称数据的假设下，我们构建了高效的多尺度展开式以求解正交径向分量，从而降低计算成本。通过解析方法与无限圆柱模型，我们对方法的数值精度进行了研究。结果表明，在低频情况下，仅需计算两个渐近项即可确保解的准确性。