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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Dirichlet-To-Neumann 映射边界条件在低频电磁问题中的应用

在本文中，我们提出了一种微分公式，结合基于 Dirichlet-to-Neumann (DtN) 算子的精确边界条件，及其在涡流问题中的应用。涡流问题的数值模型是使用简化的矢量势公式结合 DtN 算子在适当规范边界上的解析表达式得出的。与传统方法相比，这种方法的主要优点是提高了准确性并降低了计算成本。在用于预测感应电流密度分布的涡流无损检测应用中证明了所提出的公式的有效性。给出了两个模型问题的数值结果：