Contamination of the Accuracy of the Combined-Field Integral Equation With the Discretization Error of the Magnetic-Field Integral Equation

We investigate the accuracy of the combined-field integral equation (CFIE) discretized with the Rao-Wilton-Glisson (RWG) basis functions for the solution of scattering and radiation problems involving three-dimensional conducting objects. Such a low-order discretization with the RWG functions renders the two components of CFIE, i.e., the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE), incompatible, mainly because of the excessive discretization error of MFIE. Solutions obtained with CFIE are contaminated with the MFIE inaccuracy, and CFIE is also incompatible with EFIE and MFIE. We show that, in an iterative solution, the minimization of the residual error for CFIE involves a breakpoint, where a further reduction of the residual error does not improve the solution in terms of compatibility with EFIE, which provides a more accurate reference solution. This breakpoint corresponds to the last useful iteration, where the accuracy of CFIE is saturated and a further reduction of the residual error is practically unnecessary.     

The use of curl-conforming basis functions for the magnetic-field integral equation

Divergence-conforming Rao-Wilton-Glisson (RWG) functions are commonly used in integral-equation formulations to model the surface current distributions on planar triangulations. In this paper, a novel implementation of the magnetic-field integral equation (MFIE) employing the curl-conforming n~/spl times/RWG basis and testing functions is introduced for improved current modelling. Implementation details are outlined in the contexts of the method of moments, the fast multipole method, and the multilevel fast multipole algorithm. Based on the examples of electromagnetic modelling of conducting scatterers, it is demonstrated that significant improvement in the accuracy of the MFIE can be obtained by using the curl-conforming n~/spl times/RWG functions.     

Novel monopolar MFIE MoM-discretization for the scattering analysis of small objects

We present a novel method of moments (MoM)-magnetic field integral equation (MFIE) discretization that performs closely to the MoM-EFIE in the electromagnetic analysis of moderately small objects. This new MoM-MFIE discretization makes use of a new set of basis functions that we name monopolar Rao-Wilton-Glisson (RWG) and are derived from the RWG basis functions. We show for a wide variety of small objects -curved and sharp-edged-that the new monopolar MoM-MFIE formulation outperforms the conventional MoM-MFIE with RWG basis functions.     

Rigorous combined mode-matching integral equation analysis of hornantennas with arbitrary cross section

A combined rigorous method is presented for the analysis of horn antennas with arbitrary cross section and general outer surface. The horn taper is described by the mode-matching (MM) method where the cross-section eigenvalue problem is solved by a two-dimensional (2-D) finite element (FE) technique. For the exterior horn surface including the radiating aperture, the application of the Kirchhoff-Huygens principle yields two expressions for the admittance matrix which are based on the electric (EFIE) and the magnetic (MFIE) field integral equation, respectively. The equations are solved numerically by the method of moments (MoM). For the preferred EFIE formulation, the eigenvectors of the last waveguide taper section and RWG functions for triangular patches are utilized as basis-functions for the magnetic or electric surface current densities, respectively. The presented method is verified by available reference values or measurements for a waveguide radiator with a peripheral choke, a conical and a rectangular horn. Its flexibility is demonstrated at the example of a conical ridged waveguide horn     

Effect of a finite ground plane on radiated emissions from acircular loop antenna

A thin-wire circular loop antenna located above a perfectly conducting square plate is analyzed by a physical optics (PO) method. The electric field integral equation (EFIE) is solved using the method of moments to compute the current on the loop in the presence of an infinite ground plane whereby the edge effects of the plate on the loop current are neglected. The current distribution on the loop is obtained from a full-wave Fourier series analysis which requires no matrix inversion. We then use physical optics to compute the current induced on the plate in terms of the incident magnetic-field intensity. Our aim is to compare the PO solution with results obtained from a mixed wire-patch MOM code and explore its accuracy as a function of plate size and loop height. The benefits are considerable reduction in analytical and computational efforts and much less CPU time     

Linear-Linear Basis Functions for MLFMA Solutions of Magnetic-Field and Combined-Field Integral Equations

We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving closed conductors. We consider the solutions of relatively large scattering problems by employing the multilevel fast multipole algorithm. Accuracy problems of MFIE and CFIE arising from their implementations with the conventional Rao-Wilton-Glisson (RWG) basis functions can be mitigated by using the LL functions for discretization. This is achieved without increasing the computational requirements and with only minor modifications in the existing codes based on the RWG functions     

An MFIE-based tabulated interaction method for UHF terrainpropagation problems

Approximations are introduced into a magnetic field integral equation (MFIE) formulation of a two-dimensional (2-D) terrain scattering problem, which allow most of the integrals inherent in the MFIE to be performed analytically. The implementation of the method is discussed and an example is given comparing its performance against a reference solution and measured data. The new formulation applies to both TM^z and TE^z polarizations and is an improvement over the electric field integral equation (EFIE) formulation of the tabulated interaction method (TIM) in that far-field patterns can be calculated analytically leading to increased flexibility of the method     

介质体电磁散射分析中的等效偶极矩法

在介质体电磁散射分析中,提出了一种基于等效偶极矩法的快速矩阵生成技术。该方法以矩量法和RWG基函数为基础,将源点处的电(磁)流等效为电(磁)偶极子,因而阻抗矩阵元素可以认为是源点电(磁)偶极子所产生的近区场与场点电流基函数之间的相互作用。这样等效偶极矩法避免了格林函数二重积分,使得阻抗矩阵元素的生成速度明显提高。数值结果表明该方法有较高的计算效率和精度。     

基于Inagaki模式方法分析导体内谐振特性

当应用电场积分方程或磁场积分方程对导体散射特性进行矩量法分析时,在某些离散的频率点即内谐振点上,常常出现解的不稳定或不唯一情况。为了解决这一问题,该文提出了一种新型的消除内谐振的方法。这种方法基于电场积分方程,利用Inagaki模性质有效地去除了谐振模式,获得内谐振条件下正确的导体散射特性。该方法具有概念清晰和计算简便等优点。计算结果与公开发表的文献结果以及解析解相比,一致性良好。     

The corrected induced surface current for arbitrary conductingobjects at resonance frequencies

It is well known that using the method of moments in conjunction with either the electric or magnetic field surface integral equations (EFIE or MFIE) produces inaccurate surface currents on conducting bodies at resonance frequencies. A new technique (based on singular value decomposition) is developed to correct the computed current by adding a correction factor term. This term is seen to be the resonant mode current, obtained by employing the power method in the moment method matrix, multiplied by an unknown complex factor. Applying the condition of vanishing field inside the conducting object results in obtaining the unknown complex factor. Therefore, this technique is hereafter referred to as correction factor technique (CFT). When the computed surface current on a conducting sphere, proposed technique, is compared with the exact one, the numerical results show excellent agreement     

小波矩量法分析环形微带缝隙天线*

将矩量法和小波变换理论结合起来,应用于求解电磁场积分方程,分析计算了环形微带缝隙天线磁流分布、驻波、阻抗特性和辐射方向图,通过用小波基代替一般的分域基矩量法中的权函数和基函数,使矩量法中与算子相对应的阻抗矩阵变成为大量元素为零的稀疏矩阵,减小了数值方法对存储量的要求,在达到允许精度的前提下,使计算量显著降低。文中给出计算实例,验证该方法,计算结果与用一般矩量法计算结果和实际测试结果相比,吻合较好。     

A higher order parallelized multilevel fast multipole algorithm for3-D scattering

A higher order multilevel fast multipole algorithm (MLFMA) is presented for solving integral equations of electromagnetic wave scattering by three-dimensional (3-D) conducting objects. This method employs higher order parametric elements to provide accurate modeling of the scatterer's geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. This higher order scheme leads to a significant reduction in the mesh density, thus the number of unknowns, without compromising the accuracy of geometry modeling. It is applied to the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE), using Galerkin's testing approach. The resultant numerical system of equations is then solved using the MLFMA. Appropriate preconditioning techniques are employed to speedup the MLFMA solution. The proposed method is further implemented on distributed-memory parallel computers to harness the maximum power from presently available machines. Numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme     

A hybrid symmetric FEM/MOM formulation applied to scattering byinhomogeneous bodies of revolution

A new symmetric formulation of the hybrid finite element method (HFEM) is described which combines elements of the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) for the exterior region along with the finite element solution for the interior region. The formulation is applied to scattering by inhomogeneous bodies of revolution. To avoid spurious modes in the interior region a combination of vector and nodal based finite elements are used. Integral equations in the exterior region are used to enforce the Sommerfeld radiation condition by matching both the tangential electric and magnetic fields between interior and exterior regions. Results from this symmetric formulation as well as formulations based solely on the EFIE or MFIE are compared to exact series solutions and integral equation solutions for a number of examples. The behaviors of the symmetric, EFIE, and MFIE solutions are examined at potential resonant frequencies of the interior and exterior regions, demonstrating the advantage of this symmetric formulation     

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。     

Analysis of pyramidal horn antennas using moment methods

A hybrid numerical technique is developed for electrically large pyramidal horn antennas radiating in free space. A stepped-waveguide method is used to analyze the interior surfaces of the horn transition. The electric field integral equation (EFIE) is employed on the outer surfaces of the pyramidal horn including the radiating aperture. Meanwhile, the magnetic field integral equation (MFIE) is used on the aperture to relate the aperture fields and those in the horn transition The resultant hybrid field integral equation (HFIE) is solved numerically by the method of moments. This formulation is both accurate and numerically stable so that high-gain microwave pyramidal horns can be analyzed rigorously. Far-field radiation patterns, both computed and measured, are presented for three electrically-large X-band horn antennas. The comparisons demonstrate that this method is accurate enough to predict the fine pattern structure at wide angles and in the back region. Computed far-field patterns and aperture field distributions of two smaller X-band horns are also presented along with a discussion on the validity of the approximate aperture field distributions routinely used in the analysis and design of pyramidal horns     

导体目标瞬态电磁散射的时空矩量法研究

时域积分方程的矩量法是求解瞬态电磁散射的方法之一。研究了基于加权Lagurre函数和RWG基函数分别作为时间、空间基函数的时空矩量法,给出了时域磁场积分方程时空矩量法的全部计算公式,编制了相应串行和并行计算程序。计算结果表明：该方法具有很好的时域稳定特性,为宽带电磁散射分析提供了可能,同时也指出了其应用的局限性,为改进其方法提供了参考。     

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.     

Near-field to near/far-field transformation for arbitrarynear-field geometry utilizing an equivalent electric current andMoM

Presented here is a method for computing near- and far-field patterns of an antenna from its near-field measurements taken over an arbitrarily shaped geometry. This method utilizes near-field data to determine an equivalent electric current source over a fictitious surface which encompasses the antenna. This electric current, once determined, can be used to ascertain the near and the far field. This method demonstrates the concept of analytic continuity, i.e., once the value of the electric field is known for one region in space, from a theoretical perspective, its value for any other region can be extrapolated. It is shown that the equivalent electric current produces the correct fields in the regions in front of the antenna regardless of the geometry over which the near-field measurements are made. In this approach, the measured data need not satisfy the Nyquist sampling criteria. An electric field integral equation is developed to relate the near field to the equivalent electric current. A moment method procedure is employed to solve the integral equation by transforming it into a matrix equation. A least-squares solution via singular value decomposition is used to solve the matrix equation. Computations with both synthetic and experimental data, where the near field of several antenna configurations are measured over various geometrical surfaces, illustrate the accuracy of this method     

Planar near-field to far-field transformation using an equivalentmagnetic current approach

An alternative method is presented for computing far-field antenna patterns from near-field measurements. The method utilizes the near-field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna, and these currents are used to ascertain the far fields. Under certain approximations, the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near-field measurements are made. An electric field integral equation (EFIE) is developed to relate the near fields to the equivalent magnetic currents. The method of moments is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient method, and in the case of a rectangular matrix, a least-squares solution for the currents is found without explicitly computing the normal form of the equation. Near-field to far-field transformation for planar scanning may be efficiently performed under certain conditions. Numerical results are presented for several antenna configurations     

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。