跨界面目标电磁散射Sommerfeld积分的双重广义函数束拟合离散复镜像方法

A novel approach of dual GPOF/DCIM for fast computation of the sommerfeld integrals and electromagnetic scattering from an object partially embedded in dielectric half-space

混合势积分方程(mixed-potential electric field integral equation,MPIE)由于其Green函数的低阶奇异性是矩量法(MoM)等数值方法求解散射问题的主要方程.在跨界面目标的散射问题中,MPIE中的矢量势和标量势Green函数包含Sommerfeld类型的谱域积分,利用离散复镜像法(discrete compleximage method,DCIM)和Sommerfeld恒等式,将其转化为有限项复镜像Green函数的求和运算,避免了烦杂的谱域积分运算.当场点和源点位于分界面同侧时,谱函数g^(kzi)与场源位置都无关,其复指数参量可一次拟合获得,用广义函数束方法(general pencil of functions,GPOF)进行拟合.然而,当场点和源点位于分界面两侧时,谱函数与场点和源点的纵向位置(z和z′)有关.提出双重GPOF拟合方法,即将谱函数~g(kzi)对场点z分离,对有限个源区离散点z′l的谱函数用GPOF方法拟合其复镜像参量,再次使用GPOF方法拟合这些复镜像参量随z′的函数关系,则任意z′位置的复镜像参量可由函数计算直接得到,无需逐点拟合求解.对两层介质半空间环境利用双重GPOF方法、逐点GPOF方法和Sommerfeld精确积分方法分别计算,说明双重GPOF方法的有效性和准确性.本文将双重GPOF/DCIM计算跨介质分界面的理想导体球目标的散射,数值地讨论了分界面对体目标感应电流及散射的影响.

The mixed-potential integral equation （MPIE） has been usually employed in numerical approach of electromagnetic scattering of the object, such as the method of moment （MoM）, due to its low-level singularity of vector and scalar potential Green functions. When an object is embedded partially in dielectric half-space medium, the Green＇s function contains the Sommerfeld-type integrals, which embody the effect of the dielectric interface on scattering fields. Using the discrete complex image method （DCIM） and the Sommerfeld identity, the Sommerfeld integrals can be evaluated as the summation of finite complex image functions without directly numerical integration which always consumes large CPU time. As the points of the field and source are co-located in the same side of the interface, the spectrum function g （ kzp ） is not related with the field or source positions, and the complex image parameters fitted with the general pencil of functions （GPOF） method are approximate for all positions. However, if the points of the field and source are located, separately, in different sides of the interface, the spectral function is now related to z and z＇ . Generally, the GPOF is repetitiously used to find the complex image parameters for every z and z＇ , which consumes large CPU time and memory. This paper presents a novel method of Dual GPOF combining with DCIM for fast computation of the Sommerfeld integral. Firstly, the factors related with the variable z are separated, and the GPOF is used to find the complex image parameters for finite discrete source points z＇t ~ Secondly, GPOF is used again to fit the relationship of each complex image parameter with variable z＇. Then, the complex image parameter of any z＇ can be evaluated as the direct function summation, and there is no need to perform GPOF for all z＇ points. Comparing numerical values of Dual GPOF, point-by-point GPOF, and direct numerical integration, the Dual GPOF method is proved effective and efficient. Finally, Dual GPOF is applied to computation of electromagnetic scattering from a P. E.C. sphere, object partially embedded in dielectric half-space, and the scattering patterns are presented and analyzed.