Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods
Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods
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DOI：
10.1016/j.jcp.2015.02.004
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发表时间：
2015-05
期刊：
影响因子：
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通讯作者：
E. Kiliç;T. Eibert
中科院分区：
文献类型：
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作者：
E. Kiliç;T. Eibert
介绍了一种结合边界积分和有限元方法求解三维电磁介质逆散射问题的方法。基于等效原理，利用闭合曲面上未知的等效电磁表面电流密度，将介质逆问题分解为线性辐射问题和非线性空腔问题。第一个问题由一个边界积分方程表示，采用多层快速多极子方法(MLFMM)减少了计算负担。表面重建的柯西数据允许利用洛伦兹互易和Poynting定理。利用这些定理，对腔问题的噪声水平和初始猜测进行了估计。此外，还可以确定材料是否有损耗。在第二个问题中，估计的表面电流形成了空穴问题的非齐次边界条件。利用有限元技术建立空腔问题的数学模型，用高斯-牛顿法迭代求解空腔问题，重建物体的特性。第一个和第二个问题的正则化都是通过Krylov子空间方法实现的。利用合成数据和实验数据对该方法进行了测试，得到了令人满意的重建结果。
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.