Asymptotic Solution of Some Diffraction Problems
Asymptotic Solution of Some Diffraction Problems
复制标题
一些衍射问题的渐近解
DOI：
10.1002/cpa.3160090205
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
B. Seckler
中科院分区：
文献类型：
--
作者：
J. Keller;R. Lewis;B. Seckler
几位作者[1 - 151]最近讨论了一种方法，通过这种方法可以确定电磁、声波和其他线性波问题的周期解关于频率的渐近展开式。然而，实际上没有应用该方法。在本文中，我们解释的方法，并应用它来构造各种衍射问题的渐近解。其中许多问题以前没有解决。在某些情况下，我们已经解决的问题，我们验证了已知的解决方案的渐近展开与我们的渐近解相吻合，并比较精确的解决方案与前几项的渐近解的图形这里考虑的渐近展开是一个扩展的周期解关于频率的频率趋于无穷大。因此，扩展是有用的，在高频率或短波长;在电磁学中，它是有用的光学，雷达问题，等等，事实上，在扩展的领导长期只是所谓的几何光学解决方案。
Several authors [l--151 have recently discussed a method by which the asymptotic expansion with respect to frequency may be determined for periodic solutions of electromagnetic, acoustic, and other linear wave problems. However, virtually no applications of the method have been made. In the present paper we explain the method, and apply it to construct the asymptotic solutions of a variety of diffraction problems. Many of these problems have not been solved previously. In some cases where the problems have been solved we verify that the asymptotic expansions of the known solutions coincide with our asymptotic solutions and compare the exact solutions graphically with the first few terms of the asymptotic solutions.The asymptotic expansion under consideration here is an expansion of a periodic solution with respect to frequency as the frequency tends to infinity. Thus the expansion is useful at high frequencies or for short wavelengths; in electromagnetics it is useful for optics, radar problems, etc. In fact the leading term in the expansion is just the so-called geometrical optics solution.