光滑曲面上测地线射线寻迹算法及爬行波计算

Geodesic ray tracing algorithm and calculation of traveling wave on smooth surface

摘要:

提出了一种光滑凸曲面上的一致性几何绕射理论(UTD)爬行波射线寻迹算法，该算法结合泰勒级数，并根据测地线的相关性质，使用计算几何方法对暗区爬行波射线进行寻迹；在参数曲面片上根据测地线性质求解爬行波轨迹点，并对爬行波在任意一点处的测地曲率进行计算，结果准确度高。最后使用该算法结合UTD方法计算二维圆柱的散射场，得到的结果与级数解吻合，验证了本文算法的有效性，扩展了UTD方法在实际工程中的应用。

Abstract:

A creeping ray tracing algorithm of Uniform Geometrical Theory of Diffraction (UTD) method on the smooth convex surface is given. The algorithm combines with the Taylor series, and according to the related property of the geodesic, the creeping rays in shadow region are traced by computational geometry method. The discrete points of the creeping wave are obtained based on the property of geodesic on the parametric surface. The geodesic curvatures of every point at creeping wave are calculated and the high frequency results are obtained. Finally, the scattered field of two-dimensional cylinder is calculated by combining the algorithm with UTD method. The results obtained are in well agreements with the series solution, which verifies the effectiveness of the proposed algorithm. The application of UTD method in practical engineering is extended.