一维FSS电磁散射宽带特性的快速计算

基于渐近波形估计（AWE）技术和矩量法（MOM），快速分析了一维频率选择表面（FSS）的宽带电磁散射特性，首先采用MOM法将平面波照射下FSS的电场积分方程（EFIE）转化为关于感应电流的矩阵方程，并由该方程确定频率导数矩阵方程（MEFD）；再在所考虑的频带内的某一给定频率处求解MEFD，得到给定频率处的频率导数感应电流；最后根据Pade逼近理论由给定频率处的频率导数感应电流确定周期性结构在任意频率入射波照射下的感应电流，根据FSS上的感应电流及谱域Floquet谐波模计算FSS的电磁散射宽带特性，计算结果表明，AWE能有效逼近MOM逐点扫描计算的结果，同时在计算速度上可加快十几倍。     

Fast RCS computation over a frequency band using method of momentsin conjunction with asymptotic waveform evaluation technique

The method of moments (MoM) in conjunction with the asymptotic waveform evaluation (AWE) technique is applied to obtain the radar cross section (RCS) of an arbitrarily shaped three-dimensional (3-D) perfect electric conductor (PEC) body over a frequency band. The electric field integral equation (EFIE) is solved using the MoM to obtain the equivalent surface current on the PEC body. In the AWE technique, the equivalent surface current is expanded in a Taylor's series around a frequency in the desired frequency band. The Taylor series coefficients are then matched via the Pade approximation to a rational function. Using the rational function, the surface current is obtained at any frequency within the frequency range, which is in turn used to calculate the RCS of the 3-D PEC body. A rational function approximation is also obtained using the model-based parameter estimation (MBPE) method and compared with the Pade approximation. Numerical results for a square plate, a cube, and a sphere are presented over a frequency bandwidth. Good agreement between the AWE and the exact solution over the bandwidth is observed     

渐近波形估计技术在三维电磁散射问题快速分析中的应用

本文将渐近波形估计技术应用到矩量法中,计算了三维理想导体目标的宽带雷达散射截面(RCS)和单站RCS方向图.用矩量法求解电场积分方程,得到给定频率点、给定方向入射波照射下的导体表面电流密度,应用渐近波形估计技术分别得到频带内任意频率点以及任意角度入射波照射下的导体表面电流密度,进而计算出宽带RCS和单站RCS方向图.计算结果表明渐近波形估计技术与矩量法结合可以逼近矩量法逐点计算的结果,且计算效率大大提高.     

应用渐近波形估计技术快速计算宽带雷达散射截面

将渐近波形估计技术应用到矩量法中,计算了任意形状二维理想导体目标的宽带雷达散射截面.计算中使用矩量法和奇异值分解技术求解电场积分方程,得到一展开频率点的表面电流密度,通过Padé近似求出给定频带内任意频率点的表面电流密度分布,进而计算出散射场和雷达散射截面.奇异值分解技术的使用消除了电场积分方程的内谐振问题.对数值计算结果与矩量法逐点求解的结果进行了比较,两者吻合良好,且计算效率提高了约一个数量级.     

AIM结合渐近波形估计技术快速分析目标宽带电磁散射特性

该文将自适应积分方法(AIM)与渐近波形估计(AWE)技术结合快速计算了目标宽带雷达截面(RCS)。通过渐近波形技术实现快速扫频,利用自适应积分(AIM)稀疏存储稠密阻抗矩阵及阻抗矩阵的频率导数,并加速求解泰勒展开系数中的矩阵与矢量相乘计算,提高了计算速度并降低了内存需求。通过结合自动微分技术,计算了该方法所需的格林函数关于频率的高阶导数。数值结果表明,与传统AIM逐点计算相比,该方法在不失精度条件下大大地降低了计算时间。     

Fast frequency sweep technique for the efficient analysis of dielectric waveguides

This paper describes a new approach to spectral response computations of an arbitrary two-dimensional (2-D) waveguide. This technique is based on the tangential-vector finite-element method (TVFEM) in conjunction with the asymptotic waveform evaluation (AWE) technique. The former is used to obtain modes characteristics for a central frequency, whereas the latter employs an efficient algorithm to compute frequency moments for each mode. These moments are then matched via Pade approximation to a reduced-order rational polynomial, which can be used to interpolate each mode over a frequency band with a high degree of accuracy. Furthermore, the moments computations and subsequent interpolation for a given set of frequency points can be done much more rapidly than just simple simulations for each frequency point.     

周期性结构电磁感应电流宽带特性的快速计算

采用MOM法将周期结构的电场积分方程转化为关于感应电流的矩阵方程和频率导数矩阵方程，并根据Pade逼近理论由给定频率处的频率导数感应电流确定周期性结构在任一频率入射波照射下的感应电流，进而计算周期性结构的电磁感应电流宽带特性。计算结果表明，AWE在计算速度上比MOM可加快十几倍。     

Use of Asymptotic Waveform Evaluation Technique in the Analysis of Multilayer Structures With Doubly Periodic Dielectric Gratings

The reflection and dispersion characteristics of multilayer structures that involve periodically implanted material blocks are obtained by using the MoM solution of the volume integral equation. The asymptotic waveform evaluation (AWE) technique is utilized to obtain a Pade approximation of the solution in terms of a parameter such as frequency or incident angle. The use of AWE technique enables a fast sweep with respect to the approximation parameter. Moreover, a robust method for extracting the dispersion characteristics of periodic structures via Pade approximation is proposed. The AWE procedure requires the calculation of high order derivatives of the complicated kernel function that consists of Green's functions for stratified medium. These derivatives are calculated by employing the automatic differentiation theory. The reflection coefficient, propagation constant and band diagram of the structure are obtained both via point-by-point simulations and through the use of AWE technique. It is observed that AWE technique increases the computational efficiency without losing accuracy.     

Surface integral formulation for calculating conductor anddielectric losses of various transmission structures

The power-loss method, along with a surface integral formulation, has been used to compute the attenuation constant in microstrip and coplanar structures. This method can be used for the analysis of both open and closed structures. Using the surface equivalence principle, the waveguide walls are replaced by equivalent electric surface currents and dielectric surfaces are replaced by equivalent electric and magnetic surface currents. Enforcing the appropriate boundary condition, and E-field integral equation (EFIE) is developed for these currents. Method of moments with pulse expansion and point matching testing procedure is used to transform the integral equation into a matrix one. The relationship between the propagation constant and frequency is found from the minimum eigenvalue of the moment matrix. The eigenvector pertaining to the minimum eigenvalue gives the unknown electric and magnetic surface currents     

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。     

Higher order hierarchical discretization scheme for surface integral equations for layered media

This paper presents an efficient technique for the analysis of electromagnetic scattering by arbitrarily shaped perfectly conducting objects in layered media. The technique is based on a higher order method of moments (MoM) solution of the electric field, magnetic field, or combined-field integral equation. This higher order MoM solution comprises higher order curved patches for the geometry modeling and higher order hierarchical basis functions for expansion of the electric surface current density. Due to the hierarchical property of the basis functions, the order of the expansion can be selected separately on each patch depending on the wavelength in the layer in which the patch is located and the size of the patch. In this way, a significant reduction of the number of unknowns is achieved and the same surface mesh can be reused in a wide frequency band. It is shown that even for fairly large problems, the higher order hierarchical MoM requires less memory than existing fast multipole method (FMM) or multilevel FMM implementations.     

An integral transform technique for analysis of planar dielectricstructures

This paper presents a novel efficient technique for the study of planar dielectric waveguides for submillimeter-wave and optical applications. In an appropriate integral transform domain, which is determined by the Green's function of the substrate structure, higher-order boundary conditions are enforced in conjunction with Taylor expansions of the fields to derive an equivalent one-dimensional integral equation for the corresponding two-dimensional waveguide geometry. This reduction in the dimensionality of the boundary-value problem can easily be extended to three-dimensional planar structures, with equivalent two-dimensional integral equations being formulated. The reduced integral equations are solved numerically by invoking the method of moments, in which the transform-domain unknowns are expanded in a smooth localized entire-domain basis. It is demonstrated that using orthogonal Hermite-Gauss functions as an expansion basis provides very satisfactory results with only a few expansion terms. For the validation of the technique, single and coupled dielectric slab waveguides are treated     

AIM Analysis of Electromagnetic Scattering by Arbitrarily Shaped Magnetodielectric Object

A fast solution to the electromagnetic scattering by large-scale three-dimensional magnetodielectric objects with arbitrary permittivity and permeability is presented. The scattering problem is characterized by using coupled field volume integral equation (CF-VIE). By considering the total electric and magnetic fields, i.e., the sum of incident fields and the radiated fields by equivalent electric and magnetic volume currents, the CF-VIE can be established in the volume of the scatterers. The resultant CF-VIE is discretized and solved by using the method of moments (MoM). For large-scale scattering problems, the adaptive integral method (AIM) is then applied in the MoM in order to reduce the memory requirement and accelerate the matrix-vector multiplication in the iterative solver. The conventional AIM has been modified to cope with the two sets of equivalent volume currents.     

快速多极子在任意截面均匀介质柱散射中的应用

采用快速多极子法（FMM）加速后的矩量法（MoM）求解由电磁场等效原理导出的关于均匀介质柱表面等铲电磁流的积分方程,进而计算其电磁散射特性,FMM的引入使计算时间和内存开销都从O(N^2）降到O（N^3/2）,且并不增加多少复杂度。最后给出了一些介质柱体RCS的算例。     

Fast and rigorous calculation method for MoM matrix elements inplanar microstrip structures

An analytical integration technique is proposed for evaluating the elements of the impedance matrix obtained by using the spatial-domain method of moments (MoM) applied to the mixed-potential integral equation (MPIE). This technique is based on a Taylor series expansion of the integrands involving only polynomial functions, and thus allowing immediate analytical Integration     

Étude des structures planaires en très hautes fréquences par une nouvelle formulation de la méthode des moments dans le domaine spatial

An efficient analytical integration technique for computation of spatial method of moments (MoM) integrals in conjunction with numerical matched loads is presented. The current distribution on the device is solved by using the well-known Galerkin’s MoM procedure applied to mixed potential integral equation in the spatial domain. The scattering parameters are determined by considering infinite lines at each port where only the fundamental mode is assumed to propagate. The contribution of this work is the development of an integration technique for the computation of spatial domain integrals, that is fast and rigorous. This technique is based on a Taylor series expansion of the integrands involving only polynomial functions. The use of polynomial forms in the integrals leads an immediate analytical integration, and the computation time will be considerably reduced.     

Loop-tree implementation of the adaptive integral method (AIM) for numerically-stable, broadband, fast electromagnetic modeling

The adaptive integral method (AIM) is implemented in conjunction with the loop-tree (LT) decomposition of the electric current density in the method of moments approximation of the electric field integral equation. The representation of the unknown currents in terms of its solenoidal and irrotational components allows for accurate, broadband electromagnetic (EM) simulation without low-frequency numerical instability problems, while scaling of computational complexity and memory storage with the size of the problem are of the same order as in the conventional AIM algorithm. The proposed algorithm is built as an extension to the conventional AIM formulation that utilizes roof-top expansion functions, thus providing direct and easy way for the development of the new stable formulation when the roof-top based AIM is available. A new preconditioning strategy utilizing near interactions in the system which are typically available in the implementation of fast solvers is proposed and tested. The discussed preconditioner can be used with both roof-top and LT formulations of AIM and other fast algorithms. The resulting AIM implementation is validated through its application to the broadband, EM analysis of large microstrip antennas and planar interconnect structures.     

渐近波形估计技术应用于导体柱RCS方向图的快速获取

本文基于渐近波形估计(AWE)技术和矩量法(MOM)快速预测任意形状导电柱体(PEC)的单站RCS方向图.首先采用矩量法求解导体柱的电场积分方程,得到导体柱在某一给定方向入射波照射下的表面电流的低阶矩量,然后利用AWE技术求出在任意方向入射波照射下用有理分式函数表示的表面电流,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,同时在计算速度上可加快几十倍.     

渐近波形估计技术加速的频域有限差分法

本文提出了一种基于三维频域有限差分法(3D-FDFD)和渐近波形估计技术(AWE)计算三维微波结构S参数的快速算法。在分析中,将输入和输出端口的电场分别展开成某抽样频率点处的泰勒级数,通过Pad逼近及奇异值分解技术求出电场与频率的有理函数解析表达式,从而获得频带内的S参数。数值计算结果与已有结果吻台良好,并且与传统FDFD法相比,计算效率提高很多。     

Sparse matrix/canonical grid method applied to 3-D dense medium simulations

The sparse matrix/canonical grid (SMCG) method, which has been shown to be an efficient method for calculating the scattering from one-dimensional and two-dimensional random rough surfaces, is extended to three-dimensional (3-D) dense media scattering. In particular, we study the scattering properties of media containing randomly positioned and oriented dielectric spheroids. Mutual interactions between scatterers are formulated using a method of moments solution of the volume integral equation. Iterative solvers for the resulting system matrix normally require O(N/sup 2/) operations for each matrix-vector multiply. The SMCG method reduces this complexity to O(NlogN) by defining a neighborhood distance, r/sub d/, by which particle interactions are decomposed into "strong" and "weak." Strong interaction terms are calculated directly requiring O(N) operations for each iteration. Weak interaction terms are approximated by a multivariate Taylor series expansion of the 3-D background dyadic Green's function between any given pair of particles. Greater accuracy may be achieved by increasing r/sub d/, using a higher order Taylor expansion, and/or increasing mesh density at the cost of more interaction terms, more fast Fourier transforms (FFTs), and longer FFTs, respectively. Scattering results, computation times, and accuracy for large-scale problems with r/sub d/ up to 2 gridpoints, 14/spl times/14/spl times/14 canonical grid size, fifth-order Taylor expansion, and 15 000 discrete scatterers are presented and compared against full solutions.