PEC Targets Research Articles

Modified FDM with cartesian expansions for electromagnetic scattering from PEC targets

AbstractIn this article, a modified scheme of the fast dipole method (FDM) is proposed based on the Cartesian tensor. To achieve separation between the field and the source, the Taylor series used in the FDM is an incomplete second‐order expansion, which limits computational accuracy and flexibility. To address this issue, a Cartesian tensor is employed to expand the interactions between the far‐group pairs. This approach allows for a complete expansion of any order and offers flexibility in precision control, enabling a balance between computational efficiency and accuracy requirements across different application scenarios. Moreover, the computational accuracy of the proposed method can be improved without a substantial increase in time and memory requirements compared to the FDM. The validity and accuracy of the proposed method are demonstrated with numerical examples.

An AI Predictor: From Point Clouds to Scattered Far Fields for 3-D PEC Targets

An AI Predictor: From Point Clouds to Scattered Far Fields for 3-D PEC Targets

Solving Combined Field Integral Equations With Physics-Informed Graph Residual Learning for EM Scattering of 3-D PEC Targets

Solving Combined Field Integral Equations With Physics-Informed Graph Residual Learning for EM Scattering of 3-D PEC Targets

The Cylindrical Wave Approach for the Electromagnetic Scattering by Targets behind a Wall

An overview of the cylindrical wave approach in the modeling of through-wall radar problems with targets hidden behind a dielectric wall is reported. The cylindrical wave approach is a technique for the solution of the two-dimensional scattering by buried circular cross-section cylinders in a semi-analytical way, through expansion of the scattered fields into cylindrical waves. In a through-wall radar application, the scattering environment is made by a dielectric layer between two semi-infinite half-spaces filled by air. For this layout, two possible implementations of the cylindrical wave approach have been developed in the case of plane-wave excitation. The first was an iterative scheme with multiple-reflection scattered fields, and the second was a fast and non-iterative solution, through suitable basis functions (i.e., reflected and transmitted cylindrical waves). Such waves take into account all the interactions of the source field with the interfaces bounding the dielectric layers and the targets. The non-iterative approach was also extended for excitation from the radiated field by a line source. A final system was derived for the computation of the scattered field by PEC or dielectric targets. Numerical results show the potentialities of the cylindrical wave approach in the modeling of through-wall radar, in particular in the evaluation of the scattered fields by human targets in a building’s interior, modeled with a two-dimensional approach.

Integral equation‐based nonoverlapping domain decomposition method for electromagnetic scattering analysis of PEC targets in half‐space environment

AbstractAn integral equation‐based nonoverlapping domain decomposition method (IE‐NDDM) is proposed for efficient and accurate scattering analysis of electrically large PEC targets in a half‐space environment. Taking the condition that there are null fields as well as current inside PEC objects in the original problem, a novel explicit transmission condition is proposed to ensure continuity of electric currents between adjacent subdomains. Moreover, to deal with this situation that targets located in half‐space environment, the stratified‐medium dyadic Green's function is adopted. Numerical examples are provided to demonstrate the correctness and the performance of the proposed method. In detail, an analysis about electromagnetic scattering respect to the altitude of the target away from half‐space interface, the incident direction of plane wave, and the material parameters of the lower half‐space is presented; furthermore, the convergence behavior of the proposed method is studied.

Optimized cloaks made of near-zero materials for different-sized concealed targets

The optimized cloaking design for conducting cylinders of different sizes is studied based on the Mie scattering theory. We construct a concentric multi-layered cloak made of alternating materials with isotropic dielectrics and epsilon-near-zero (ENZ) material, the thickness of which can be determined through genetic algorithm. As the radius of the conducting cylinder increases, high order scattering contributions are becoming evident, and more layers are needed. The scattering cross sections of three different radii of PEC cylinders are minimized by utilizing different numbers of multi-layers respectively. We find that eight or less optimized layers can cancel most of the scattering from a conducting cylinder with its dimension compared to wavelength, and more effectively when taking the ENZ material as the inner starting shell. The frequency dependence of total scattering is also studied, leading to the result that the bandwidth decreases as the size of concealed PEC cylinder increases. Furthermore, it is shown that the cloaking efficiency is less sensitive to the permittivity and thickness of the ENZ material, due to the small phase variation in the ENZ material. The multi-layered cloak designed for a PEC target can also be used to evidently reduce the scattering of a dielectric core and design a multi-layered elliptical cloak.

Reliable approach for bistatic scattering of three-dimensional targets from underlying rough surface based on parabolic equation**Project supported by the National Natural Science Foundation of China (Grant No. 61771407).

A parabolic equation (PE) based method for analyzing composite scattering under an electromagnetic wave incidence at low grazing angle, which composes of three-dimensional (3-D) electrically large targets and rough surface, is presented and discussed. A superior high-order PE version is used to improve the accuracy at wider paraxial angles, and along with the alternating direction implicit (ADI) differential technique, the computational efficiency is further improved. The formula of bistatic normalized radar cross section is derived by definition and near-far field transformation. Numerical examples are given to show the validity and accuracy of the proposed approach, in which the results are compared with those of Kirchhoff approximation (KA) and moment of method (MoM). Furthermore, the bistatic scattering properties of composite model in which the 3-D PEC targets on or above the two-dimensional Gaussian rough surfaces under the tapered wave incidence are analyzed.

High-Order Sparse Shape Imaging of PEC and Dielectric Targets Using TE Polarized Fields

In this paper, we present a novel method for microwave imaging using sensors with transverse electric (TE) polarization. The method is applicable to metallic and dielectric objects and exploits the sparseness of the sought solution, by imposing a measurement model based on multipole sources. In order to verify the achievable performance, the method has been numerically tested against different scenarios, including targets with complex concave cross sections as well as multiple objects. The investigation has shown that, opposite to the transverse magnetic (TM) polarization, the standard (zero order) sparse processing yields no or very little information about the targets. In contrast, using higher order multipole sources to build the sparse imaging dictionaries allows retrieving complicated target shapes, even in presence of noise. In addition, we have compared the reconstruction results obtained using the TE and TM polarization.

Compressed sensing based fast method of solving the electromagnetic scattering problems for threedimensional conductor targets

The method of moments is one of the most commonly used algorithms for analyzing the electromagnetic scattering problems of conductor targets. However, it is difficult to solve the matrix equation when analyzing the electromagnetic scattering problem of the electric large target. In recent years, the theory of the compressed sensing was introduced into the method of moments to improve the computation efficiency. The random selected impedance matrix is used as a measurement matrix, and the excitation voltage is used as a measurement value when using compressed sensing theory. The recovery algorithm is used to solve the induced current of target. The method can avoid the inverse problem of matrix equation and improve the computational efficiency of the method of moments, but it can be applied only to 2-dimensional or 2.5-dimensional target. The application of compressed sensing needs to know the sparse basis of the current in advance, but the induced current of three-dimensional target which is expressed by an Rao-Wilton-Glisson basis function is not sparse on the commonly used sparse basis, such as discrete cosine transform basis and discrete wavelet basis. To solve this problem, a method of combining compressed sensing with characteristic basis functions is proposed to analyze the electromagnetic scattering problem of three-dimensional conductor target in this paper. The characteristic basis function method is an improved method of moments. The target is divided into several subdomains, the main characteristic basis functions are comprised of current bases arising from the self-interactions within the subdomain, and the secondary characteristic basis functions are obtained from the mutual coupling effects of the rest of the subdomains. Then a reduction matrix is constructed to reduce the order of matrix equation, and the current can be expressed by the characteristic basis function and its weighting coefficient. In the method presented in this paper, the weighting coefficient is considered as a sparse vector to be solved when the characteristic basis function is used as sparse basis. The number of weighting coefficients is less than the number of unknown ones, so it can be obtained from the compressed sensing recovery algorithm. At the same time, the generalized orthogonal matching pursuit algorithm is used as the recovery algorithm to speed up the recovery process. Finally, the proposed method is used to calculate the radar cross sections of a PEC sphere, nine discrete PEC targets and a simple missile model. The numerical results validate the accuracy and efficiency of the method.

Electromagnetic Scattering Characteristics of Rough PEC Targets in the Terahertz Regime

To deal with the perfect electric conductor rough targets’ scattering problem, which is the basic premise of the radar applications at terahertz frequencies, a hierarchical semideterministic modeling and full-wave-algorithm-based computation method was proposed. The scattering fields with phase information and synthetic aperture images of electrically large cubes with different surface characteristics were obtained. The influence of the surface roughness can be easily observed. According to the imaging results, we can predict that other than the scattering calculation challenges caused by the surface roughness, it also brings great benefits that more detailed information about the targets will emerge on the images.

A Hybrid 3DMLUV-FIA Method for Scattering from a 3D Dielectric Object above a 2D Dielectric Rough Surface

The electromagnetic scattering from the composite model of a three-dimensional (3D) dielectric object located above a two-dimensional (2D) dielectric rough surface is analyzed in this work. Poggio, Miller, Chang, Harrington, Wu, and Tsai (PMCHWT) integral equations are discretized by the method of moments (MoM) into a matrix which is solved by Biconjugate Gradients Stabilized (BICGSTAB) method. Method of 3DMLUV was used for PEC object located above rough surface. Comparing to the case when object and rough surface are both PEC, the memory requirement and computational complexity for dielectric models are increased due to doubled unknown number. Moreover, compared to dielectric object in free space, the coupling between dielectric object and dielectric rough surface will result in complicated numerical simulation. To solve this problem, the updated rank based 3D Multilevel UV (3DMLUV) method is employed to reduce memory consumption and CPU time overhead. The 3DMLUV has been successfully applied in the scattering of PEC targets; however, when the object or rough surface becomes dielectric, the coupling between dielectric object and dielectric rough surface will lead to slow constriction. Therefore, the Fast Iterative Approach (FIA) is applied to further speed up the constricted speed of the matrix required in 3DMLUV. The efficiency, stability, and accuracy of the proposed method are demonstrated in a variety of scattering problems.

Evaluation of Scattering From Electrically Large and Complex PEC Target Coated With Uniaxial Electric Anisotropic Medium Layer Based on Asymptotic Solution in Spectral Domain

This paper presents a novel and original approach for the evaluation of electromagnetic (EM) scattering from electrically large and complex target coated with uniaxial electric anisotropic medium (UEAM) layer. The evaluation includes two indispensable aspects, the geometry modeling of the target and the determination of the surface currents. Once the equivalent surface currents (ESCs) induced on the outer surface of the coated target are determined, the scattered field could be calculated by the corresponding radiation integrals. First, the outer surface of the arbitrarily shaped target is discretized using flat triangle facets. Second, the ESCs on any facet are deduced from the surface fields, which involve a complicated coupling of type I and type II waves existing in the UEAM. Thus, the determination of the surface fields and the ESCs on the surface of the target with large radius of curvature is the crux of the whole evaluation. By making the tangent plane approximation, used in the physical optics (PO) method, any discretized flat facet could be approximated as an infinite PEC plate coated with a homogenous UEAM layer. Thereafter, the scattering from the infinite coated plate is asymptotically calculated by using the proposed spectral domain method combined with saddle point evaluation (SDM-SPE). Ultimately, comparisons of the proposed asymptotic solution with the reference solutions calculated numerically confirm the validity and efficiency of the proposed SDM-SPE. Numerical results of several canonical and complex targets coated with UEAM layer are given by the proposed approach for the first time.

A Novel Multilevel Matrix Compression Method for Analysis of Electromagnetic Scattering From PEC Targets

We present a new multilevel matrix compression method (MLMCM) and its application to the analysis of scattering problems from three-dimensional (3-D) arbitrary-shaped conductors. The compression is achieved without generating the full subblocks of the matrix by the rank-based method. Unlike the conventional rank-based method, incoming compression matrix and outgoing compression matrix are defined when coupling with a cluster of its far interaction groups. Only a small translation matrix is redefined for every two coupling groups. The merits of the proposed method are: 1) it is kernel function-independent and can be applied to arbitrary complex media; 2) it is more efficient than conventional rank-based methods. This paper shows numerical results to demonstrate the validity of the proposed method.

Simulation of EM Scattering from 3-D Target by MOM with Pulse Basis Function

In this paper, electromagnetic (EM) scattering from a 3-D PEC target is simulated. The method of moments (MOM) with the pulse basis function and the point matching technique is presented to solve the magnetic field integral equation (MFIE). The flat triangular patch is applied to subdivide the surface of the 3-D target, and the surface unknowns are the arbitrary orthogonal unit vector of the triangular patch. Validity of this algorithm is shown by comparing the E plane and H plane radar cross section (RCS) from a sphere or a cylinder to those results of MOM with the RWG vector basis function. It is necessary to note that computational time of the algorithm presented in this paper is less than the MOM with the RWG(Rao Wilton Glisson) basis function.

Bistatic scattering from three-dimensional target on perfectly conducting rough surface by using G-SMFSIA/CAG

This paper presents a novel and powerful numerical technique called general sparse-matrix flat-surface iterative approach-canonical grid (G-SMFSIA/CAG), which combines the sparse-matrix flat-surface iterative approach-canonical grid (SMFSIA/CAG) for 2D conducting rough surface and the method of moment (MoM) based on Rao-Wilton-Glisson (RWG) function for PEC target, to compute the electromagnetic scattering from a three-dimensional PEC target on conducting rough surface. The coupling surface integral equations (SIEs) for the composite model are derived based on Huygens surface equivalence principle. The SMFSIA/CAG is applied to solve the SIE of rough surface, and the targets’ SIE is solved using MoM. The iteration of SMFSIA/CAG and MoM takes account the interactions between target and the rough surface. Combining the PM(Pierson-Moskowitz)sea surface generated using Monte-Carlo method, the bistatic scattering coefficient for different targets on sea surface are computed. Convergence and effectivity of the G-SMFSIA/CAG is numerically validated. The bistatic scattering coefficient from ship on sea surface is calculated finally,and the dependence of bistatic scattering pattern upon the wind speed is discussed.

EM Scattering from a PEC Target Below the Layered Rough Surface Based on the Cross Coupling Iterative Approach

EM Scattering from a PEC Target Below the Layered Rough Surface Based on the Cross Coupling Iterative Approach

TE Versus TM for the Shape Reconstruction of 2-D PEC Targets Using the Level-Set Algorithm

The transverse electric (TE) polarization for shape reconstruction of perfect electric conducting 2-D targets is presented. The deformation velocity for the TE polarization case is implemented in the level-set algorithm. A comparison between the reconstruction CPU time between the TE and transverse magnetic (TM) polarizations is discussed. The numerical results show that retrieving the shape and location of multiple targets of arbitrary cross sections becomes computationally intensive when illumination with TE-polarized waves is used. If the orientation of the unknown cylinders is a priori known, the TM-polarized waves provide faster reconstruction results with the same accuracy compared with the TE-polarized waves. Upon corrupting the synthetic data with Gaussian noise up to signal-to-noise ratio of 5 dB, the TM polarization seems to provide more accurate results compared with the TE case.

THE LEVEL SET SHAPE RECONSTRUCTION ALGORITHM APPLIED TO 2D PEC TARGETS HIDDEN BEHIND A WALL

The level set algorithm is extended to handle the reconstruction of the shape and location of objects hidden behind a dielectric wall. The Green's function of stratifled media is used to modify the method of moments and the surface integral equation forward solver. Due to the oscillatory nature of the Sommerfeld integrals, the stationary phase approximation is implemented here to achieve fast and accurate reconstruction results, especially when the targets are located adequately far from the wall. Transverse Magnetic (TM) plane waves are employed for excitation with limited view for transmitting and receiving the waves in the far fleld at one side of the wall. The results show the capability of the level set method for retrieving the shape and location of multiple 2D PEC objects of arbitrary shapes even when there are located at a small distance from the wall. To reduce the computational expenses of the algorithm in the case of multiple hidden objects, the MPI parallelization technique is implemented leading to a reduction in the CPU time from hours on a single processor to few minutes using 128 processors on the NCSA Supercomputer Center.

Surface impedance modeling of PEC targets: application to shape reconstruction

We consider the inverse electromagnetic scattering problem of retrieving the shape of an inaccessible, perfectly electric conducting target from a set of far field measurements and develop a new reconstruction method in which the unknown scatterer is modeled by means of a surface impedance. The basic idea is to approximate the unknown object through a circular impedance cylinder enclosed in it and equipped with a suitable inhomogeneous surface impedance. By doing so, the ill-posedness and the nonlinearity of the underlying problem are then handled separately, through two successive processing steps. In the first step, the inhomogeneous surface impedance of the auxiliary scatterer is reconstructed through the regularized analytical continuation of the measured far-field data. Then, the unknown shape is retrieved through the solution of a nonlinear optimization problem aimed at determining the spatial locations where the field outside of the impedance target vanishes, in agreement with the boundary condition arising onto the unknown target. As demonstrated with several numerical results, the method is robust against uncertainties on data and provides quite accurate results for targets with starlike boundaries having both convex and concave parts.

A hybrid MM‐PO method combining UV technique for scattering from two‐dimensional target above a rough surface

AbstractIn this article, an efficient hybrid MM‐PO method combining UV technique is applied to calculate the EM scattering from a 2D PEC target above a PEC rough surface. Considering the target as the MM region and the rough surface as the PO region, the current on the rough surface is obtained through the PO approximation, leaving only unknowns on the target region. Furthermore, a UV technique is used to accelerate the coupling interaction between the target and the rough surface. With this hybrid method, large scale target/rough surface scattering problems can be solved more effectively. Using the Monte‐Carlo method to generate the rough surface, the bistatic difference field radar cross‐section of the target above a Pierson‐Morkowitz rough surface is numerically simulated. The results show good agreement when compared with the other methods. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2957–2960, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22922