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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.
The high-order window function combined with fractional expansion technique is used to study and establish a fast and efficient algorithm for the dyadic Green’s function of the electromagnetic field in a layered anisotropic medium.Firstly, by using the high-order window function, Sommerfeld The integrals are transformed into integrals on the generalized fast-descent path, and a new higher-order power series expansion and a strict Lommel function expression for the Hankel transform of high-order window functions are given to meet the requirements of high-precision computation in full space Based on this, the integral path is divided into a series of small areas by using the zero point of Bessel function and the integrated value of each small area is determined by the improved adaptive Gauss quadrature formula, and then the continuous expansion method is introduced Summing the integral values in each interval, so that the convergence efficiency of the entire integral is greatly improved.Finally, the numerical results verify the effectiveness of the proposed method.