In this paper, a perfectly matched layer (PML) method is proposed to solve the time-domain electromagnetic scattering problems in 3D effectively. The PML problem is defined in a spherical layer and derived by using the Laplace transform and real coordinate stretching in the frequency domain. The well-posedness and the stability estimate of the PML problem are first proved based on the Laplace transform and the energy method. The exponential convergence of the PML method is then established in terms of the thickness of the layer and the PML absorbing parameter. As far as we know, this is the first convergence result for the time-domain PML method for the three-dimensional Maxwell equations. Our proof is mainly based on the stability estimates of solutions of the truncated PML problem and the exponential decay estimates of the stretched dyadic Green's function for the Maxwell equations in the free space.

中文翻译：

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时域电磁散射问题PML方法的收敛性分析

在本文中，提出了一种完美匹配层（PML）方法来有效解决 3D 中的时域电磁散射问题。PML 问题在球层中定义，并通过使用拉普拉斯变换和频域中的实坐标拉伸导出。首先基于拉普拉斯变换和能量方法证明了PML问题的适定性和稳定性估计。然后根据层的厚度和 PML 吸收参数建立 PML 方法的指数收敛。据我们所知，这是3维麦克斯韦方程组时域PML方法的第一次收敛结果。