二维亥姆霍兹方程在半空间中瑞利高频理论的推广：无穷远处辐射条件和一维周期性不均匀边界上狄利克雷条件
Generalization of Rayleigh's high-frequency theory for the 2D Helmholtz equation in a half-space subject to a radiation condition at infinity and a Dirichlet condition on a 1D periodically-uneven boundary
浏览论文内容
中文总结 AI 辅助
研究二维亥姆霍兹方程相关物理问题，重新审视瑞利通过正弦形边界的衍射理论及微扰方法，修正并推广该方法，以求解任意入射角及任意形状一维周期性不可穿透边界的情况。
中文摘要 AI 辅助
二维亥姆霍兹方程、辐射条件和狄利克雷边界条件，在数学上对应至少三个二维物理问题，用于预测不可穿透的一维周期性不均匀边界一侧的总标量波场，比如平面 TE 电磁波撞击边界等情况。瑞利首次尝试非启发式解决此类问题。本文将重新审视瑞利通过正弦形不可穿透边界的衍射理论，特别是其高频 regime 中获得衍射问题数学显式解的微扰方法。将修正并推广该方法以获得任意入射角及任意形状一维周期性不可穿透边界的解。
英文摘要
The 2D Helmholtz equation, radiation condition and Dirichlet boundary condition, are the translation, in mathematical terms, of (at least) three physical 2D problems for the prediction of the total scalar wavefield on one side of an impenetrable 1D periodically uneven boundary when: a) a plane TE electromagnetic wave propagating in the vacuum strikes the boundary the other side of which is occupied by a perfectly-conducting medium, b) a plane SH elastic elastic wave strikes a rigid boundary, c) a plane acoustic wave strikes a pressure-release boundary. The first attempt to solve such problems in a non-heuristic manner was made by Lord Rayleigh (in his book, 'The Theory of Sound' which appeared in 1896). My task will be to revisit Rayleigh's theory of diffraction by a sinusoidal-shaped, impenetrable boundary, and more specifically, his perturbation method for obtaining a mathematically-explicit solution to the diffraction problem in the high-frequency regime. In so doing, I shall correct and generalize Rayleigh's method to obtain solutions for arbitrary angles of incidence as well as for 1D periodic impenetrable boundaries of quite-general shape.
