2-D validation of a formulation for the analysis of 3-D bodies thatare periodic in one direction and finite sized in the others

A numerical scheme to analyze three-dimensional bodies that are periodic in one direction (z) and finite sized in the other ones (x, y) is presented. The geometry and material composition of the body can be arbitrary. A new formulation using the conjugate gradient-fast Fourier transform method (CG-FFT) has been developed. The formulation is based on the discretization and resolution of the electric field integral equation (EFIE) in both the real and spectral domains and leads to an efficient and accurate numerical procedure. Results are presented for RCS, equivalent currents and fields inside 3-D periodic structures (infinitely long cylinders with arbitrary shape and material composition). These results are compared with analytical solutions and the agreement is found to be good     

Analysis of Electromagnetic Scattering from Plasma Antenna Using CG-FFT Method

A gaseous plasma column as an efficient radiator of electromagnetic waves is well known. This paper presents the scattering analysis of a plasma antenna using the conjugate gradient fast Fourier transform (CG-FFT) method. Radar cross sections (RCS) of designed plasma antenna for different plasma parameters are computed mainly. Numerical results show that the plasma antenna with appropriate parameters can offer lower RCS than the metal one. It is evident from the observed scattering characteristics that the plasma antenna can be regarded as a rod of imperfect conductor with losses.     

Spectral domain analysis of conducting patches of arbitrarygeometry in multilayer media using the CG-FFT method

A conjugate gradient-fast Fourier transform (CG-FFT) scheme for analyzing finite, flat, metallic patches in multilayer structures is presented. Rooftop and razor-blade functions are considered as basis and testing functions, respectively. An equivalent periodic problem in both domains (real and spectral) is obtained and solved. Aliasing problems are avoided by performing a window on the Green's function. The spectral domain periodicity makes it feasible to take into account almost all the harmonics and to reduce the ripple in the computed current distributions. Nearly all the operations are performed in the spectral domain, including Green's function computations. Several results of convergence rates, current distributions and radar cross-section (RCS) values are given and compare favorably with measurements or results obtained by other methods     

同心导体圆盘-圆环结构散射场的一种分析方法

本文从电场积分方程出发,经傅氏变换,并分离出电荷对散射场的贡献,导出了平面波投射于同心圆盘-圆环结构时,分析散射场的一个形式简单且便于求解的积分方程。当平面波正投射时解法尤为简单。据此求解圆盘和/或圆环结构上感应电流分布和相应的散射场。为验证本方法的准确性,对圆盘雷达散射截面(RCS)的计算结果与精确解进行了比较,结果吻合很好。文中还给出了当平面波正投射时,同心圆盘-圆环结构上感应电流各分量的幅度分布和散射场分布。     

ANALYSIS OF THE SCATTERING OF RIVET ON AIRCRAFT

This letter investigates the scattering characteristic of the rivets on aircraft.The electric Field Integral Equation (EFIE)is used with the moment to calculate the current distribution on the surface of the rivet.With the application of Gaussian integral corresponding triangular cell,the time to fill the Z matrix is greatly reduced.Finally,the RCS of a type of rivet on aircraft is analyzed.     

广义Cauchy技术加速MOM对介质柱单站RCS的快速求解

本文基于Cauchy技术和矩量法（MOM）快速预测任意截面形状、非均匀介质柱体的单站雷达散射截面（RCS）。首先采用MOM求解介质柱的电场积分方程,得到介质柱在某一给定方向入射波照射下的各低阶矩量的极化电流,然后利用Cauchy技术获得用有理函数模型表示的、在任意角度入射波照射下的极化电流,进而计算出RCS的宽角响应。计算结果表明,Cauchy技术守全能逼近MOM精确计算的曲线,同时可大大加快计算速度。     

Combining the Higher Order Method of Moments With Geometric Modeling by NURBS Surfaces

This paper introduces the nonuniform rational B-spline (NURBS) surfaces to improve the geometric modeling of the higher order method of moments (MoM). The electric field integral equation (EFIE) is discretized by the hierarchical higher order basis functions and converted to a matrix equation. Then the elements of the impedance matrix are efficiently evaluated by a new set of formulas. The bistatic radar cross sections (RCS) obtained by this new technique are compared with those obtained by the commonly used higher order MoM. The example of a cylinder and a missile shows excellent accuracy of the NURBS surfaces and that of the resultant RCS. Moreover, this new technique can fully exploit the flexibility of the higher order basis functions when the surface is highly curved, whereas the commonly used higher order MoM can not.      

Planar near-field to far-field transformation using an array ofdipole probes

A method is presented for computing far-field antenna patterns from measured near-field data measured by an array of planar dipole probes. The method utilizes the near-field data to determine some equivalent magnetic current sources over a fictitious planar surface which encompasses the antenna. These currents are then used to find the far fields. The near-field measurement is carried out by terminating each dipole with 50 Ω load impedances and measuring the complex voltages across the loads. An electric field integral equation (EFIE) is developed to relate the measured complex voltages to the equivalent magnetic currents. The mutual coupling between the array of probes and the test antenna modeled by magnetic dipoles is taken into account. The method of moments with Galerkin's type solution procedure is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient-fast Fourier transformation (CG-FFT) method exploiting the block Toeplitz structure of the matrix. Numerical results are presented for several antenna configurations to show the validity of the method     

Analysis of arbitrary metallic surfaces conformed to a circularcylinder using the conjugate gradient-fast Fourier transform (CG-FFT)method

An efficient scheme for analyzing electrodynamic problems involving arbitrary metallic surfaces conformed to a circular cylinder, using the conjugate-gradient-fast-Fourier-transform (CG-FFT) method, is presented. The numerical method outlined is efficient in CPU time and minimizes the memory storage requirements. Several results are presented and compared with numerical or measured values that appear in the literature     

外推技术结合矩量法应用于二维介质柱RCS计算

基于Richardson外推(Extrapolation)提出了一种提高精度和快速计算任意二维介质柱体的雷达散射截面(RCS)外推技术和矩量法(MOM)相结合的方法(RE—MOM)。首先用二层粗细有序网格对介质柱体截面剖分。接着采用矩量法对相应二维介质柱体的电场积分方程求解，得到介质体在某一平面入射波照射下各自的电场向量，通过外推技术获得介质柱体在这一人射波照射下细网格上高精度的电场向量，进而计算出RCS。文中计算了几个例子，并与其他数值计算方法进行了比较，结果表明RE—MOM方法是正确和有效的。     

Scattering from 3-D cavities with a plug and play numerical schemecombining IE, PDE, and modal techniques

In this paper, we present a multidomain and multi-method coupling scheme called FACTOPO, based on generalized scattering matrix computations on three-dimensional (3-D) subdomains. The global target Ω is split in N_V subdomains (V_i)(i=1, N_V), separated by N_I fictitious surfaces (Γ _j)(j=1,N_I). We use a modal representation of the tangent fields on the interfaces. In each domain, the generalized scattering matrix S_i is computed with different methods such as the 3-D finite-element method (FEM) or the electric field integral equation (EFIE). This coupling scheme leads to an important reduction in computational resources, especially for cavities with one dimension much larger than the other two. The advantages of this formulation for parametric studies is illustrated by two cases: computing the RCS of an air-intake terminated with a flat PEC or a fan (CHANNEL) and of an antenna structure coupled to an electronic feed with a varying parameter (DENEB). Numerical as well as experimental results are presented     

Combining the moment method with geometrical modelling by NURBSsurfaces and Bezier patches

Induced current distributions on conducting bodies of arbitrary shape modelled by NURBS (non uniform rational B-splines) surfaces are obtained by using a moment method approach to solve an electric field integral equation (EFIE). The NURBS surfaces are expanded in terms of Bezier patches by applying the Cox-de Boor transformation algorithm. This transformation is justified because Bezier patches are numerically more stable than NURBS surfaces. New basis functions have been developed which extend over pairs of Bezier patches. These basis functions can be considered as a generalization of “rooftop” functions. The method is applied to obtain RCS values of several objects modelled with NURBS surfaces. Good agreement with results from other methods is observed. The method is efficient and versatile because it uses geometrical modelling tools that are quite powerful     

Stable and accelerated procedure to calculate transient scattering using electric field integral equation

A stable and accelerated procedure for the electric field integral equation (EFIE) is developed. The procedure employs an implicit method in conjunction with a time averaging scheme to solve EFIE with the second-order time derivatives. Two examples are provided to demonstrate the superior stability and efficiency of the proposed procedure.     

渐近波形估计技术用于介质柱宽角度RCS的计算

基于渐近波开估计（AWE）技术和矩量法（MOM）快速预测任意形状非均匀介质柱体的单站雷达散射截面RCS方向图,采用矩量法求解介质柱的电场积分方程,得到介质柱在某一给定方向入射波照射下的极化电流,然后利用AWE技术将任一角度入射波照射下的极化给定角度附近展开成Taylor级数,通过Pade逼近将Taylor级数转化为有理函数,由此可获得介质柱在任一角度入射波照射下的极化电流,进而计算出RCS方向图。计算结果表明AWE完全能逼近MOM精确计算的曲线,同时可加快计算速度。     

磁场积分方程矩量法中基函数的立体角修正

本文通过考察电磁散射问题矩量法求解中电场积分方程和磁场积分方程的公式 ,分析了在使用三角屋顶基函数情况下传统的磁场积分方程在计算带有棱角的电小尺寸金属物体雷达截面时存在的不足 ,提出了一种基函数的立体角修正技术 ,从而达到了减小计算误差的目的。计算结果表明了算法的有效性。     

预处理结合AWE技术求解导体目标RCS

采用渐近波形估计技术(AWE)和预处理技术求解导体目标的宽带雷达散射截面(RCS)。应用矩量法求解导体目标的电场积分方程,通过构造预条件算子,使由矩量法得到的阻抗矩阵稀疏化,从而计算导体表面电流时变得简便,再结合渐近波形估计(AWE)技术计算导体目标的宽带雷达散射截面(RCS)。实例结果表明,该方法在计算电大导体目标时具有较高的计算效率和很好的精度。     

高阶矩量法求解MFIE 时近奇异性提取*

采用高阶矩量法求解磁场积分方程时,相邻面片之间的互阻抗是一个难以算准的奇异性四重积分,因为内层面积分和外层面积分中同时包含有奇异性.本文对于内层的近奇异积分采用sinh (x)函数作积分变换,而对于外层的弱奇异性积分采用Duffy变换进行处理,使得被积式变成能够直接数值积分的连续光滑函数.数值结果表明该方法计算近奇异积分时精度远高于直接高斯积分方法,求得的雷达散射截面与电场积分方程所得的结果完全一致,验证了方法的准确性和有效性.     

基于Laguerre多项式的边界积分方程时域求解

针对时域积分方程中存在的晚时震荡问题,介绍了基于Laguerre多项式的电场、磁场和混合场积分方程,求解了导体球和导体圆柱的时域电流分布和后向散射场以及单站RCS。结果表明,3种积分方程很好地解决了晚时震荡问题,混合场积分方程具有更高的计算精度。     

A combined full-wave CG-FFT method for rigorous analysis of largemicrostrip antenna arrays

An accurate and efficient technique is presented for the analysis of large microstrip antenna arrays. The technique consists of an amalgamation of a spatially discrete scheme, consisting of the CG-FFT method and the complex discrete image (CDI) technique. The unique feature of this approach is the use of the spatially discrete CG-FFT for analyzing microstrip structures. The aliasing and truncation errors are thoroughly eliminated in this approach. In addition, the grad-div operators are transformed from singular Green's functions to differentiable expansion and testing functions by using Galerkin's procedure, thereby improving the accuracy and the rate of convergence. To show the accuracy and efficiency of this technique, a number of microstrip arrays, including a large microstrip reflectarray, have been studied. It is found that the simulations carried out using this technique are in very good agreement with measurements     

A Scheme for Analyzing the RCS of a Scale Model Beyond the Size Measureable in the Range of Millimeter-Wave

The problem of obtaining the radar cross section (RCS) of a scale model too large to measure in the range of millimeter-wave by measurement is investigated. This topic, to the best of our knowledge, has been little investigated due to its complexity. A scheme named RCS part measurement and synthesis to this problem is developed in this paper. This method combines measurement with theoretical calculation. The first step in using the method is that a scale model is partitioned into several parts measurable. Then the contributions of the sections and shadow region shadowed by all other parts are removed from the measured RCS data of every part. Finally, the scattered fields of all the parts are synthesized to obtain the total RCS of the scale model by means of the technique of relative phase synthesis. A result is presented to illustrate the utility of this scheme.