The time domain linear sampling method (TD-LSM) solves inverse scattering problems using time domain data by creating an indicator function for the support of the unknown scatterer. It involves only solving a linear integral equation called the near-field equation using different data from sampling points that probe the domain where the scatterer is located. To date, the method has been used for the acoustic wave equation and has been tested for several different types of scatterers, i.e. sound hard, impedance, and penetrable, and for wave-guides. In this paper, we extend the TD-LSM to the time dependent Maxwell's system with impedance boundary conditions - a similar analysis handles the case of a perfectly electrically conducting (PEC) body. We provide an analysis that supports the use of the TD-LSM for this problem, and preliminary numerical tests of the algorithm. Our analysis relies on the Laplace transform approach previously used for the acoustic wave equation. This is the first application of the TD-LSM in electromagnetism.

翻译：时间域线性取样方法(TD-LSM)通过为未知散射器提供支持而设定一个指标函数,从而用时间域数据解决反散射问题。它只涉及使用探测散射器所在区域的取样点的不同数据解决称为近场方程式的线性整体方程式。迄今为止,该方法一直用于声波方程式,并测试了几种不同类型的散射器,即声音硬性、阻力和穿透性,以及波导。在本文中,我们将TD-LSM扩展至具有阻力性边界条件的依赖于时间的马克斯韦的系统――一个类似的分析处理一个完全进行电动操作的(PEC)体。我们提供了一种分析,支持对该问题使用TD-LSM,以及算法的初步数字测试。我们的分析依赖于以前用于声波方程式的Laplace变换法。这是电磁学中TD-LSM的第一个应用。