论文标题
介电障碍物散射问题和对反问题的应用的光谱准确方法
A spectrally accurate method for the dielectric obstacle scattering problem and applications to the inverse problem
论文作者
论文摘要
我们分析了从嘈杂的远场数据的知识中重建三维均质介电障碍物的形状的逆问题。向前问题通过第二种边界积分方程的系统解决。对于这些耦合积分方程的数值解，我们通过将这些方程运输到单位球体上提出了快速光谱算法。我们回顾边界对远场运算符的不同性能，并给出第一个Fréchet衍生物的伴随操作员的表征。使用这些结果，我们讨论了迭代正规化高斯 - 牛顿方法的实现，以实现反问题的数值解，并为星形障碍物提供数值结果。
We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations. For the numerical solution of these coupled integral equations we propose a fast spectral algorithm by transporting these equations onto the unit sphere. We review the differentiability properties of the boundary to far field operator and give a characterization of the adjoint operator of the first Fréchet derivative. Using these results we discuss the implementation of the iteratively regularized Gauss-Newton method for the numerical solution of the inverse problem and give numerical results for star-shaped obstacles.
