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Abstract-This article proposes a new scheme of real-coefficient fitting both Green's function and its gradient with Fast Fourier Transform (RFGG-FG-FFT) for combined field integral equation (CFIE) to compute the conducting object's electromagnetic scattering, which improves original fitting both Green's function and its gradient with Fast Fourier Transform (FGG-FG-FFT) on efficiency. Firstly, based on Moore-Penrose generalized inverse, an equivalent form of fitting matrix equation is obtained containing the property of Green's function's integral proved by addition theorem. Based on this property, with truncated Green's function new fitting technique is presented for computing fitting coefficients with real value expression, which is different from complex value expression by the original fitting technique in FGG-FG-FFT. Numerical analysis of error shows that new fitting technique has the same accuracy, but only one half of sparse matrices' storage compared to the original fitting technique in FGG-FG-FFT. Finally, the new scheme combining FGG-FG-FFT and new fitting technique is constructed. Some examples show that the new scheme is accurate and effective compared to FGG-FG-FFT and p-FFT.

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An efficient hybrid SIE-KA-FMM method is presented to analyze the electromagnetic scattering from combined conducting and dielectric objects above the rough surface. In this approach, the induced electric current on the rough surface is obtained by the Kirchhoff approximation (KA). The single integral equation (SIE) method is utilized to efficiently compute scattering from the composite target with markedly reducing the numbers of unknowns compared with the conventional coupled integral equation method. The fast multi-pole method (FMM) is incorporated for faster operation and less memory requirement. Several examples verify the validation of the hybrid SIE-KA-FMM method. The composite scattering characteristics of diversiform targets above the rough surface are obtained. Moreover, the numerical results with the different permittivity of dielectric part, polarization mode, working frequency, root mean square (RMS) and correlation length of rough surface, incident pitching/azimuth angle, and target height and target category have been analyzed to provide some useful conclusions. INDEX TERMS Kirchhoff approximation, single integral equation, fast multi-pole method, combined conductor and dielectric objects, rough surface, composite scattering.

The composite electromagnetic (EM) scattering characteristics of low-altitude target above valley composite rough surface are studied. The composite rough surface modeling theory is adopted to simulate the natural cavity structure of valley environment. Aiming at efficiently and accurately calculate the composite EM scattering from low-altitude target above valley environment, a hybrid method combining shooting and bouncing ray (SBR) technique and equivalent edge currents (EEC) method is proposed, in which SBR method based on the ray-density normalization (RDN) is applied to consider the multiple interactions between target and environment, and EEC method meliorates target's edge diffraction. Numerical examples illustrate the efficiency and validation of proposed hybrid method. Finally, based on the hybrid SBR-EEC method, the EM scattering characteristics of low-altitude target above valley environment are further investigated to show scattering mechanisms of this composite model and provide some useful conclusions through physical phenomena.INDEX TERMS Valley composite rough surface, shooting and bouncing ray technique, equivalent edge currents method, composite electromagnetic scattering.