Generalization of the surface-volume-surface electric field integral equation (SVS-EFIE) for the solution of electromagnetic scattering problems on 3-D dielectric objects embedded in multilayered media is proposed. While having only a single unknown surface current density on the boundary of the scatterer, the SVS-EFIE also features only electric field dyadic Green’s functions in its integral operators. This property in conjunction with Michalski–Zheng’s formulation of the multilayered media electric field Green’s function allows for the formulation of SVS-EFIE in the mixed potential form for the solution of the scattering problems in layered media. In the proposed method of moments (MoM) discretization scheme, the gradient and divergence operators associated with the electric field Green’s function are shifted to the basis and test functions of the discretized integral operators. As a result, the proposed formulation features no derivatives acting on the components of the layered media dyadic Green’s function, hence, substantially alleviating the numerical evaluation of the pertinent Sommerfeld integrals. The proposed MoM formulation scalarizes reaction integrals containing the multilayered media dyadic Green’s function through the use shape function-based definition of the basis and test functions. The resultant MoM integrals feature no singularities stronger than $1/R$ . The validation of the proposed SVS-EFIE formulation and its MoM discretization is performed through a comparison of the computed fields against the fields produced using commercial electromagnetic analysis software.

Surface-Volume-Surface Electric Field Integral Equation for Solution of Scattering Problems on 3-D Dielectric Objects in Multilayered Media

The surface-volume-surface electric field integral equation (SVS-EFIE) is generalized for the case of scattering problems on the composite nonmagnetic dielectric objects situated in planar nonmagnetic layered medium. The piece-wise homogeneous regions of the scatterer can be arbitrarily positioned with respect to the layers of stratification. The SVS-EFIE being a class of single-source integral equations is formed by restricting the surface single-source electric field representation in each distinct region of the scatterer through the volume-EFIE (V-EFIE) enforced on the boundary of that region for only the tangential component of the total field. As a result, the SVS-EFIE utilizes only the electric field dyadic Green's functions. This allows for its cast into the mixed-potential form using classical Michalski–Zheng's formulation and method of moments (MoM) discretization featuring easily computable integrals with singularities no stronger than $1/R$ , $R$ being the distance from the source to the observation point in such integrals. The matrices of MoM discretization are represented in hierarchical form (as $\mathcal {H}$ -matrices) enabling solution of the scattering problems in multilayered media with $O(N^\alpha \log N)$ CPU time and memory complexities, where $\alpha$ is a geometry-dependent constant ranging from 1 to 1.5 depending on the shape of the scatterer. While the MoM surface and volume meshes discretizing the regions of the scatterer are constructed to ensure that no mesh element crosses interfaces between the layers, the clusters of both the surface and volume elements in their respective recursive partitionings in the process of $\mathcal {H}$ -matrix construction are allowed to span multiple layers of the medium. Upon computation of the layered medium Green's function kernels with the discrete complex image method allowing clusters of elements to cross dielectric interfaces between the layers is shown to preserve compressibility of the corresponding $\mathcal {H}$ -matrix blocks.

Surface-Volume-Surface EFIE for Electromagnetic Analysis of 3-D Composite Dielectric Objects in Multilayered Media

An efficient approach to analyze the electromagnetic (EM) scattering from coated objects above a three-dimensional (3-D) dielectric random rough surface is proposed in this paper. The elect...

Electromagnetic scattering of coated objects over sea surface based on SBR-SDFSM

A new shooting and bouncing ray (SBR) simulator based on the hybrid scheme of GO/PO/SDFM/EEC method is developed for the accurate prediction of composite scattering from a low altitude target above the electrically very-large-scale sea surface. It can adequately deal with the complex local electromagnetic interactions between the target and the large scope sea surface. The method is compared with the exact computational electromagnetic solver FEKO-MLFMM to validate its accuracy and efficiency. Then, it is applied to simulate the bistatic and monostatic scattering characteristics of an airplane above the electrically large sea surface at X-band, for different sea states. The results reveal the contributions from the target, sea surface, and interactions, which are of significance for radar target detection and remote sensing in real maritime environments.

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A New Shooting Bouncing Ray Method for Composite Scattering from a Target above the Electrically Large Scope Sea Surface

A microwave scattering model is proposed for the ground surface covered with multilayers vegetation. The vegetation leaves are simulated with the discrete elliptical particles in layers, which are randomly distributed above the randomly rough surface. The finite element method is applied to solve the scattering magnetic field equation based on the Dirichlet boundary, and the relationship between the radar cross section and bidirectional reflectance distribution function is deduced with the coherent scattering field. The internal mechanism of microwave scattering of multilayers vegetation is explored with the numerical results, and the relationship of vegetation growing parameter with scattering characteristic is established.

Electromagnetic Scattering of Rough Ground Surface Covered by Multilayers Vegetation

This paper proposes a hybrid method for computing electromagnetic scattering from target above composite rough surface of ground and near sea in adjacent region. First, a kind of composite rough su...

A hybrid method for electromagnetic scattering from target above composite rough surface of ground and near sea in adjacent region

This article proposes a hybrid iterative solver for modeling composite rough surface electromagnetic scattering. First, a kind of divisional rough surface with the shape of a round water zone embed...

High Efficiency Iterative Solver for Modeling Composite Rough Surface Electromagnetic Scattering

A hybrid method of single integral equation and the electric/magnetic current combined field integral equation (JMCFIE) is proposed, abbreviated as SJMCFIE, for analyzing scattering from composite conductor and dielectric objects. Fitting Green’s function with fast Fourier transform (FG-FFT) is adopted to combine SJMCFIE to lastly formulate SJMCFIE-FG-FFT for reducing computation complexity of resultant matrix-vector multiplications further. Next, scattering from the composite hemisphere is computed to verify SJMCFIE-FG-FFT on memory storage, computation efficiency compared to SJMCFIE-MLFMA. Simultaneously, comparison of FG-FFT and the other FFT-based algorithms being combined with SJMCFIE shows that SJMCFIE-FG-FFT is insensitive to grid spacing, easy implementation, and high accuracy. Besides, SJMCFIE-FG-FFT also can be used for analyzing scattering from the coated structure.

Analysis of scattering from composite conductor and dielectric objects using single integral equation method and FG-FFT

The electromagnetic (EM) scattering characteristics of target above coastal environment are complicated due to the simultaneous existence of ground region and sea region. Nevertheless, the actual target possesses both conducting part and dielectric part. Such a composite scattering problem involves multiple media parameters and large amount of unknowns. Hence, aiming at accurately and efficiently calculating the EM scattering from combined conducting and dielectric target above coastal environment, the hybrid SIE-KA method is introduced in which single integral equation (SIE) method is utilized to reduce the number of combined target's unknowns and Kirchhoff approximation (KA) is applied to obtain induced electric and magnetic current on the surface of coastal environment. Moreover, multilevel fast multipole algorithm (MLFMA) is adopted to significantly reduce the computational cost and memory requirement. Several numerical examples demonstrate the accuracy and efficiency of the hybrid method. Finally, the EM scattering characteristics of combined conducting and dielectric target above coastal environment have been studied. The radar cross section (RCS) curves with different category of environment, polarization mode, working frequency, statistic parameters of coastal environment, permittivity of target's dielectric part, target's height and target category have been analyzed in detail to provide some useful conclusions. The approach and results can be broadly applied in remote sensing simulation of coastal environment with combined target.

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Research on Electromagnetic Scattering Characteristics of Combined Conducting and Dielectric Target Above Coastal Environment

A generalized hybrid scheme combining finite element method (FEM) and the method of moments (MoM) accelerated by multilevel fast multipole algorithm (MLFMA) is first presented to investigate scattering from a 3-D dielectric object above a 2-D electrically large dielectric rough surface. The hybrid FEM/ MoM scheme is divided into the FEM region for the object based on Helmholtz's equation and the MOM region for the rough surface based on coupled integral function, which can greatly reduce the computed region. MLFMA is employed to reduce computation complexity of MOM region itself and coupling interaction matrices between MOM region and FEM region. Consequently the iterative solving process can be greatly accelerated. This genralized hybrid FEM/MOM is very suitable for investigating scattering characteristics of composite model composed of a complex material object and electrically large dielectric rough surface. Some examples verify this generalized hybrid FEM/MOM features high efficiency, low storage requirement, high accuracy and generality.

Hua Long Sun

Papers

A hybrid method for electromagnetic scattering from target above composite rough surface of ground and near sea in adjacent region

High Efficiency Iterative Solver for Modeling Composite Rough Surface Electromagnetic Scattering

Analysis of scattering from composite conductor and dielectric objects using single integral equation method and FG-FFT

Research on Electromagnetic Scattering Characteristics of Combined Conducting and Dielectric Target Above Coastal Environment

An improved hybrid FEM/MOM combining MLFMA for composite electromagnetic scattering