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

Abstract

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′l. 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.