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为了克服传统离散复镜像法计算有耗媒质中索莫菲尔德积分的不足,提出了一种基于增强离散复镜像法的插值算法。当场点和源点位于分界面两侧时,谱域格林函数中同时包含场点和源点位置坐标,传统二级离散复镜像法无法一次拟合复指数参数,考虑将谱域核函数对场点坐标分离,然后建立复镜像参数随源点坐标的一维插值表,从而可以对复镜像参数进行插值运算;当场点和源点均位于有耗媒质中时,二级离散复镜像法的采样路径会带来错误,提出对谱域核函数进行形式变换再进行求解,从而使插值法适合有耗媒质中格林函数的计算;为了扩大传统二级离散复镜像法的横向计算距离,在对复镜像参数进行复指数级数拟合时,选择增强离散复镜像法的采样路径。该方法同传统对格林函数进行插值的方法相比,在计算复杂度降低的同时,效率和精度都获得了大大提高。
In order to overcome the shortcomings of the traditional discrete complex image method for calculating the Somolfeld integral in the lossy medium, an interpolation algorithm based on enhanced discrete complex image method is proposed. When the spot and the source point are located on both sides of the interface, the spectral Green’s function contains both the location of the field point and the source point. The traditional two-stage discrete complex image method can not fit the complex exponential parameter once. Point coordinates, and then establish a one-dimensional interpolation table of the complex image parameters with the coordinates of the source point, so that interpolation operations can be performed on the complex image parameters. When both the spot point and the source point are in the lossy medium, the samples of the second level discrete complex image method The path will lead to errors. It is proposed that the spectral kernel function be transformed formally and then be solved, so that the interpolation method is suitable for the Green’s function in lossy media. In order to enlarge the horizontal distance of traditional two-level discrete complex image method, When the parameters of image are fitted by complex exponential series, the sampling path of enhanced discrete complex image method is selected. Compared with the traditional interpolation method for Green’s function, this method has greatly improved the efficiency and precision while reducing the computational complexity.