论文标题
从扰动形状本身的边界测量中重建障碍物的小扰动
Reconstructing Small Perturbations of an Obstacle for Acoustic Waves from Boundary Measurements on the Perturbed Shape Itself
论文作者
论文摘要
我们得出了无法穿透的障碍物的形状变形与散射场本身上散射场的边界测量之间的关系。我们的推导是基于层电位技术和场扩展（FE）方法（正式推导）的系统方式进行严格的。我们扩展了这些技术，以从障碍物的微小扰动以及DNO或NDO在扰动的形状上的障碍物和边界测量的形状变形之间的微小扰动以及障碍物变形之间的关系，从而得出了dirichlet to-neumann（DNO）（DNO）和Neumann-to-Dirichlet（NDO）操作员的渐近扩展。所有关系都使我们采用了非常有效的算法，以确定障碍物形状扰动的低阶傅立叶系数。
We derive relationships between the shape deformation of an impenetrable obstacle and boundary measurements of scattering fields on the perturbed shape itself. Our derivation is rigourous by using systematic way, based on layer potential techniques and the field expansion (FE) method (formal derivation). We extend these techniques to derive asymptotic expansions of the Dirichlet-to-Neumann (DNO) and Neumann-to-Dirichlet (NDO) operators in terms of the small perturbations of the obstacle as well as relationships between the shape deformation of an obstacle and boundary measurements of DNO or NDO on the perturbed shape itself. All relationships lead us to very effective algorithms for determining lower-order Fourier coefficients of the shape perturbation of the obstacle.
