周期表面中局部扰动的重建
Reconstruction of Local Perturbations in Periodic Surfaces
AI总结：
本文研究周期结构中局部扰动的逆散射问题，提出基于Floquet-Bloch变换的数值方法，通过初始化定位扰动支持域并结合牛顿-共轭梯度法求解优化问题，实现扰动的有限样条基函数近似。
摘要：
本文研究周期结构中局部扰动的逆散射问题。不同于传统周期问题，散射场的周期性不再成立，因此经典方法不再适用。基于Floquet-Bloch变换，开发了一种数值方法解决正向问题，从而为逆问题设计算法提供可能。该方法包含两个步骤：第一步是初始化，通过简单方法定位扰动支持域，将无限域逆问题转化为一个周期单元问题；第二步是应用牛顿-共轭梯度法求解相关优化问题。扰动随后通过有限样条基函数进行近似。文中最后给出了数值示例，展示了该数值方法的有效性。
英文摘要：
This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet-Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, shows the efficiency of the numerical method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
