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An efficient method for the solution of the inverse scattering problem for penetrable obstacles

机译:解决可穿透障碍物反散射问题的一种有效方法

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We consider a two-dimensional scattering problem for inhomogeneous media. This problem arises from the study of time-harmonic electromagnetic scattering problems for Transverse Magnetic (TM) waves. In the direct scattering problem we have to compute the scattered wave from the knowledge of the incident wave and of the inhomogeneity. In the inverse scattering problem we have to reconstruct the refractive index of the inhomogeneity from some knowledge of the scattered waves generated by the inhomogeneity itself with known incident waves. The complete formulation of this inverse problem is given by a system of two integral equations, where the unknown functions are the refractive index of the inhomogeneity, and the total field inside the inhomogeneity. Note that, the total field is defined as the sum of the incident field plus the scattered field. The numerical solution of this system has a high computational cost even for low or medium size discretization schemes. The main contribution of the present paper is given by an efficient method for the numerical solution of this problem, where, roughly speaking, the computation of the total field inside the inhomogeneity is avoided. Some numerical experiments are used to show the performance of the proposed method. In these experiments, we have used exact scattering data, and synthetic scattering data.
机译:我们考虑非均匀介质的二维散射问题。这个问题来自对横向电磁(TM)波的时谐电磁散射问题的研究。在直接散射问题中,我们必须根据入射波和不均匀性的知识来计算散射波。在逆散射问题中,我们必须根据不均匀性本身与已知入射波所产生的散射波的一些知识来重构不均匀性的折射率。这个反问题的完整表述由两个积分方程组给出,其中未知函数是不均匀性的折射率和不均匀性内部的总场。注意,总场定义为入射场与散射场之和。该系统的数值解法即使对于中小型离散方案也具有很高的计算成本。本文的主要贡献是通过一种有效的方法对该问题进行了数值求解,从总体上讲,避免了计算不均匀内部的总场。通过一些数值实验证明了该方法的有效性。在这些实验中,我们使用了精确的散射数据和合成散射数据。

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