This paper concerns the numerical resolution of a data completion problem for the time-harmonic Maxwell equations in the electric field. The aim is to recover the missing data on the inaccessible part of the boundary of a bounded domain from measured data on the accessible part. The non-iterative quasi-reversibility method is studied and different mixed variational formulations are proposed. Well-posedness, convergence and regularity results are proved. Discretization is performed by means of edge finite elements. Various two- and three-dimensional numerical simulations attest the efficiency of the method, in particular for noisy data.

中文翻译：

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麦克斯韦方程组数据完成问题的拟可逆方法的数值解析

本文涉及电场中时谐麦克斯韦方程组数据完成问题的数值分辨率。目的是从可访问部分的测量数据中恢复有界域边界的不可访问部分的丢失数据。研究了非迭代准可逆性方法，并提出了不同的混合变分公式。证明了适定性，收敛性和规律性结果。离散化是通过边缘有限元进行的。各种二维和三维数值模拟证明了该方法的有效性，特别是对于嘈杂的数据。