In this article, we present a differential formulation combined with an exact boundary condition based on a Dirichlet-to-Neumann (DtN) operator, and its applications to eddy current problems. A numerical model for the eddy current problem is derived using a reduced vector potential formulation combined with analytic expression of a DtN operator on an appropriate canonical boundary. The main advantage of this method is the improved accuracy and reduced computational cost compared to conventional approaches. The effectiveness of the proposed formulation is demonstrated in eddy current nondestructive testing applications for predicting the induced current density distribution. The numerical results for two model problems are presented: a conducting sphere in a uniform magnetic field and an eddy current probe inspection of a conducting plate with a volumetric defect.

中文翻译：

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狄利克雷-诺伊曼图边界条件在低频电磁问题中的应用


在本文中，我们提出了一种与基于狄利克雷到诺伊曼 (DtN) 算子的精确边界条件相结合的微分公式，及其在涡流问题中的应用。使用简化矢量势公式并结合适当规范边界上的 DtN 算子的解析表达式，导出了涡流问题的数值模型。与传统方法相比，该方法的主要优点是提高了精度并降低了计算成本。所提出的公式的有效性在用于预测感应电流密度分布的涡流无损检测应用中得到了证明。给出了两个模型问题的数值结果：均匀磁场中的导电球和具有体积缺陷的导电板的涡流探头检查。