水平层状各向异性介质中电磁场并矢Green函数的一种高效算法

利用高阶窗函数结合连分式展开等技术研究并建立一种水平层状各向异性介质中电磁场并矢Green函数的快速有效算法. 首先借助于高阶窗函数将构成并矢Green函数的Sommerfeld积分转化成广义快速下降路径上积分，并给出高阶窗函数Hankel变换的一种新的更高阶幂级数展开式以及严格的Lommel函数表达式，以满足在全空间上高精度计算并矢Green函数的要求. 在此基础上，用Bessel函数的零点将积分路径划分成一系列小区间并通过改进的自适应Gauss求积公式确定各个小区间上的积分值，然后引入连分式展开法对各个区间上的积分值求和，从而使整个积分的收敛效率得到大大提高. 最后通过数值结果验证本方法的有效性. 关键词： 高阶窗函数 连分式展开 并矢Green函数 层状各向异性介质

An efficient algorithm of the electromagnetic dyadic green's function in a horizontal-layered anisotropic medium

In this paper, we advance an efficient algorithm of electromagnetic spatial dyadic Greens function in a horizontal-layered anisotropic medium through high order window function and so on. First, we use the high order window function to transform the Sommerfeld integrals of dyadic Greens function into integrals along a generalized steep descent path. And we give a new and higher order of power series of expansion expression of Hankel transforms of the window function and an accurate formula of Lommel function so that the dyadic Greens function can be precisely computed either near or far from the transmitter. Then, we divide the integral path into a series of subintervals based on the zeros of Bessel function and compute integral per subinterval using an improved adaptive Gauss quadrature. Furthermore, an algorithm of the finite continued fraction expansion is used to sum up the integrals on each subinterval to greatly accelerate the convergence velocity of the numerical integration along the descent path. Finally, our numerical results validated the efficiency of the algorithm.