On the use of SVD-improved point matching in the current-modelmethod [EM scattering]

An approach which uses the singular value decomposition (SVD) to improve the accuracy of the numerical solution obtained with fictitious current models is introduced. In this approach, the SVD is essentially facilitating a systematic way to optimally reduce the generalized inverse matrix used in the solution to a submatrix of smaller rank. This reduction strikes a balance between the fulfillment of the boundary conditions at the matching points and that between them. Clearly, the boundary conditions errors at the matching points are no longer strictly zero. However, the previously discernible errors between the matching points are markedly suppressed. The approach is efficacious not only when the impedance matrix is inherently singular or highly ill conditioned, but also when this matrix is entirely well conditioned. It can be generalized and implemented in any method of moments code which uses point matching for testing. The approach has been incorporated into an existing solution based on the current-model method for the problem of scattering from periodic sinusoidal surfaces, and is shown to render the solution more accurate     

A comparison of spherical wave boundary value matching versus integral equation scattering solution for a perfectly conducting body

A spherical-wave expansion (SPEX) technique for calculating the scattering from a smooth perfectly conducting body is presented. Sample case results are compared with the well-known Lawrence Livermore National Laboratory Numerical Electromagnetics code (NEC), which is based on the integral equation formulation. The internal fields are computed for both results using a third surface current integration program, which is totally independent of both SPEX and NEC. The internal fields, which would be zero for a perfect solution, are much more sensitive to the currents than the scattered fields. The SPEX solution, which uses fewer unknowns and less computer time than NEC, also produces a lower internal field. The SPEX technique also allows a direct check on satisfaction of the boundary condition at any set of points on the surface, independent of the points used to obtain the solution. This provides a valuable built-in test feature for quickly validating results, which is one of the most attractive features of the technique.     

A hybrid moment method solution for TEz scattering fromlarge planar slot arrays

This paper develops a hybrid moment method (MM) based numerical model for electromagnetic scattering from large finite-by-infinite planar slot arrays. The model incorporates the novel concept of a physical basis function (PBF) to reduce dramatically the number of required unknowns. The model can represent a finite number of slot columns with slots oriented along the infinite axis, surrounded by an arbitrary number of coplanar dielectric slabs. Each slot column can be loaded with a complex impedance to tailor the array's edge currents. An individual slot column is represented by equivalent magnetic scattering currents on an unbroken perfectly conducting plane. Floquet theory reduces the currents to a single reference element. In the array's central portion, where the edge perturbations are negligible, the slot column reference elements are combined into a single basis function. Thus, one PBF can represent an arbitrarily large number of slot columns. A newly developed one-sided Poisson sum formula is used to calculate the mutual coupling between the PBF and the slot columns in the presence of a stratified dielectric media. The array scanning method (ASM) gives the mutual coupling between the individual slot columns. The hybrid method is validated using both numerical and experimental reference data. The results demonstrate the method's accuracy as well as its ability to handle array problems too large for traditional MM solutions     

An exact solution of the generalized exponential integral and itsapplication to moment method formulations

The generalized exponential integral is one of the most fundamental integrals in antenna theory and for many years exact solutions to this integral have been sought. This paper considers an exact solution to the generalized exponential integral which is completely general and independent of the usual restrictions involving the wavelength, field point distance and dipole length is considered. The exact series representation presented converges rapidly in the induction and near-field regions of the antenna, and therefore provides an alternative to numerical integration. Two method of moments formulations are considered. They use the exact expression for the generalized exponential integral in the computation of the impedance matrix elements. It is demonstrated that, for very thin straight-wire antennas, an asymptotic expansion can be used to obtain a numerically convenient form of the generalized exponential integral     

A new solution for TE plane-wave scattering from a symmetricdouble-strip grating composed of equal strips

The paper presents a new rigorous solution for the problem of TE plane-wave scattering from a periodic planar symmetric double-strip grating, i.e., the grating which has two equal strips per unit cell. The grating is placed at a dielectric interface and is assumed to be perfectly conductive and infinite in length and width. The formulation is based on a multimode equivalent network representation and the relevant integral equation defined on two separate intervals is rigorously solved by reducing to two simpler equations with known solutions. From this a new simple analytic expression is obtained for the coupling matrix elements which involves no integration. Some computations based on this new expression are carried out and the results are compared to those obtained by the Riemann-Hilbert method and also to some of the previously obtained single-strip results in the limiting case     

A periodic moment method solution for TM scattering from lossydielectric bodies with application to wedge absorber

The periodic moment method (PMM) solution for the scattering from two-dimensional lossy dielectric bodies is developed. The purpose is to design a microwave wedge absorber for low reflectivity so that one can improve the performance of anechoic chamber measurements. With PMM, the reflection and transmission coefficients of periodically distributed bodies illuminated by a plane wave have been accurately calculated using a Cray Y-MP supercomputer. Through these studies, some wedge absorber configurations have been designed, fabricated, and then tested in the OSU/ESL compact range measurement facility. Two 8-in commercial wedges, a curved wedge, and a four-layer wedge, were studied. In all cases, good agreement between calculations and measurements was obtained     

3-D computation of E fields by the volume-surface integral equation(VSIE) method in comparison with the finite-integration theory (FIT)method [clinical hyperthermia application]

An algorithm has been developed for calculation of 3-D electric (E) fields by the volume-surface integral equation (VSIE) method. Integration over surface elements is performed using elementary analytical formulas, assuming a linear interpolation of surface charges. Grid points at electrical interfaces are split off, taking into account the E field behavior at these contours, specifically at sharp bends and multimedia junctions. Averaging procedures are utilized in order to avoid undefined or infinite values at critical points. The VSIE is solved by iteration using the GMRES (general minimum residuum) solver on a SUN workstation SPARC-IPX or Cray XMP, whereby convergence speed decreases considerably as the heterogeneity of the problem increases. Results for 3-D test cases (plane wave illuminating a layered cylinder) generally agree well with the finite-integration-theory (FIT) method if high E field gradients occur perpendicular to electrical boundaries. The VSIE method predicts slightly higher E fields only in critical regions. On the other hand, the FIT method at present is more efficient with respect to computation time for large domains with high cell numbers (>100000 cells)     

A multilevel formulation of the method of moments [EM scattering]

The modeling of electromagnetic scattering and radiation problems using the method of moments (MoM) is limited to resonant frequencies because of the extensive computational requirements of solving large matrix equations. In this study, a multilevel formulation of MoM which allows substantial computational savings and, thus, extends the application of MoM to higher frequencies is presented. Using a hierarchy of discretization levels, the multilevel technique extracts different modal components of the solution by focusing on a specific portion of the spectrum of the solution at a given level. The fundamental features of this process for the MoM solution of the electric field integral equation (EFIE) are developed and implemented. This multilevel MoM allows the rapid evaluation of the current distributions on a variety of 2-D scatterers with thousands of unknowns in fewer than ten cycles and in fractions of the normal CPU times. The method is stable, fast, suitable for multiple excitations, and adaptable as a `solve' module for almost any MoM code     

On the variational aspects of the moment method [electromagnetics]

The variational properties of the moment method as applied via the electric field integral equation (EFIE) to perfectly conducting radiators and scatterers with time-harmonic excitation are discussed. It is shown that the admittance, impedance, gain and radar cross-section can be expressed in terms of the self-reaction or the mutual reaction of the electric current distribution induced on the body. Subject to the above restrictions and assuming the usual reciprocity theorems are applicable, it is shown that the reaction is stationary with Galerkin's method, but it is not when the non-Galerkin moment method is applied in the customary manner. Numerical results are included to compare the performance of the variational and nonvariational moment method     

Coupling finite element and integral equation solutions usingdecoupled boundary meshes [electromagnetic scattering]

A method is outlined for calculating scattered fields from inhomogeneous penetrable objects using a coupled finite element-integral equation solution. The finite element equation can efficiently model fields in penetrable and inhomogeneous regions, while the integral equation exactly models fields on the finite element mesh boundary and in the exterior region. By decoupling the interior finite element and exterior integral equation meshes, considerable flexibility is found in both the number of field expansion points as well as their density. Only the nonmetal portions of the object need be modeled using a finite element expansion; exterior perfect conducting surfaces are modeled using an integral equation with a single unknown field since E _tan is identically zero on these surfaces. Numerical convergence, accuracy, and stability at interior resonant frequencies are studied in detail     

A weak form of the conjugate gradient FFT method fortwo-dimensional TE scattering problems

The problem of two-dimensional scattering of a transversal electric polarized wave, by a dielectric object is formulated in terms of a hypersingular integral equation, in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free-space Green's function and the contrast source over the domain of interest. A weak form of the integral equation for the unknown electric flux density is obtained by testing it with rooftop functions. The vector potential is expanded in a sequence of the rooftop functions and the grad-div operator is integrated analytically over the dielectric object domain only. The method shows excellent numerical performance     

A versatile moment method solution of the conventional and modifiedcoplanar waveguide T-junctions

The conventional and modified coplanar waveguide (CPW) T-junctions, both symmetric and nonsymmetric, are investigated using the full wave moment method with duality for the electric and magnetic currents. The method is shown to be accurate and computationally more efficient than the finite-difference-time-domain (FDTD) method previously used to solve these T-junctions. The results show that the dispersion in the S-parameters of the different types of CPW T-junctions investigated can be minimized by a proper choice of the dimensions and locations of the air bridges. The versatility of the method is demonstrated by its ability to solve complicated CPW structures with different types of air bridges, such as the modified CPW T-junction     

矩量法精确求解磁场积分方程的有效方法

矩量法求解磁场积分方程（MFIE)迭代收敛快,但计算精度不高. 通过提取和处理MFIE积分核中的强奇异点,并采用积分域变换消除方程中残留弱奇异性的方法,使矩量法求解MFIE能达到良好的精度. 计算了模型的雷达散射截面（RCS）MFIE计算结果与电场积分方程（EFIE）结果吻合良好,误差小于0.5 dB,且收敛性优于EFIE,验证了算法的有效性.     

Regularization of the moment matrix solution by a nonquadraticconjugate gradient method

Inspired by Tikhonov regularization, a nonlinear conjugate gradient method is proposed with the purpose of simultaneously regularizing and solving the moment matrix equation. The procedure is based on a nonquadratic conjugate gradient algorithm with exact line search, restart, and rescale. Applied to the problem of TM scattering by perfectly conducting rectangular cylinders, the method is shown to exhibit a fast convergence rate     

Development and numerical solution of integral equations forelectromagnetic scattering from a trough in a ground plane

We develop a set of scalar integral equations that govern the electromagnetic scattering from a two-dimensional (2-D) trough in an infinite perfectly conducting ground plane. We obtain accurate and efficient numerical solution to these equations via the method of moments (MoM). Our numerical implementation compares favorably to popular methods such as the finite element/boundary integral (FE/BI) method, generalized network formulation (GNF), and electric field integral equation (EFIE) techniques     

改进的SUSAN角点提取算法

采用了一种改进的SUSAN角点提取算法。SUSAN角点提取算法主要利用了角点周边的纹理分布特性,即在角点的某个区域内的像素灰度与角点的相似性来完成角点的提取。在此理论基础上,研究了一种新的基于SUSAN理论的改进的SUSAN角点提取算法,该算法利用了角点附近像素灰度的纹理特征来完成角点的提取,即通过控制与核心点相似的点的连通性与数量来确定该点是否为角点。并且针对阈值T固定选取的问题,采用了一种自动选取阈值的新方法。为了进一步验证所提取角点的实用性,利用特征点匹配对其进行了匹配验证。并通过仿真实验对其进行了检验。     

一种动态特征匹配的部分重叠点云配准方法

点云配准方法能够有效地完成对不同重叠率、不同规模点云间的配准,可确保三维重建模型的精度。针对该问题,提出一种动态特征匹配的部分重叠点云配准方法,首先基于欧氏距离分割法将点云分割为子点云;然后提取子点云特征,考虑到不同点云的规模不同,提取的特征规模也是不同的,提出利用动态时间规整算法(DTW)完成子点云间的映射;最后利用迭代配准算法求取拼接点云间的平移、旋转矩阵,利用该矩阵完成点云间的配准和拼接。实验结果表明,提出的方法能够有效地解决部分重叠点云和不同规模点云的配准问题。