High-Frequency Wave Propagation by the Segment Projection Method
High-Frequency Wave Propagation by the Segment Projection Method
复制标题
DOI：
10.1006/jcph.2002.7033
复制
发表时间：
2002-05
影响因子：
4.1
通讯作者：
B. Engquist;O. Runborg;A. Tornberg
中科院分区：
文献类型：
--
作者：
B. Engquist;O. Runborg;A. Tornberg
几何光学是用于高频波传播近似的标准技术。基于偏微分方程的计算方法取代了传统的光线追迹法，近年来已被应用于几何光学。这些新方法具有许多优点，但通常表现出与波的线性叠加的困难。本文介绍了一种新的基于相空间分段投影法的偏微分技术。叠加问题得到了很好的解决，焦散线附近振幅的计算问题也得到了很好的解决。其计算复杂度与射线追踪的计算复杂度是同一数量级。新的算法进行了描述，并给出了一些计算实例，包括模拟波导。
Geometrical optics is a standard technique used for the approximation of high-frequency wave propagation. Computational methods based on partial differential equations instead of the traditional ray tracing have recently been applied to geometrical optics. These new methods have a number of advantages but typically exhibit difficulties with linear superposition of waves. In this paper we introduce a new partial differential technique based on the segment projection method in phase space. The superposition problem is perfectly resolved and so is the problem of computing amplitudes in the neighborhood of caustics. The computational complexity is of the same order as that of ray tracing. The new algorithm is described and a number of computational examples are given, including a simulation of waveguides.