ABSTRACT This paper deals with the reconstruction of small-amplitude perturbations in the electric properties (permittivity and conductivity) of a medium from boundary measurements of the electric field at a fixed frequency. The underlying model is the three-dimensional time-harmonic Maxwell equations in the electric field. Sensitivity analysis with respect to the parameters is performed, and explicit relations between the boundary measurements and the characteristics of the perturbations are found from an appropriate integral equation and extensive numerical simulations in 3D. The resulting non-iterative algorithm allows to retrieve efficiently the centre and volume of the perturbations in various situations from the simple sphere to a realistic model of the human head.

中文翻译：

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3D Maxwell 方程的灵敏度分析及其在解决固定频率逆介质问题中的应用

摘要 本文涉及从固定频率下电场的边界测量重建介质的电特性（介电常数和电导率）的小幅度扰动。基础模型是电场中的三维时谐麦克斯韦方程组。对参数进行敏感性分析，并从适当的积分方程和广泛的 3D 数值模拟中找到边界测量值与扰动特征之间的明确关系。由此产生的非迭代算法允许有效地检索各种情况下扰动的中心和体积，从简单的球体到真实的人类头部模型。