金属-各向异性介质体组合目标频域体表积分方程矩量法

利用体表积分方程矩量法求解了具有任意的介电常数张量和磁导率张量的各向异性介质与金属的组合目标的电磁散射问题.给出了基于RWG面基函数和SWG体基函数的体表积分方程阻抗矩阵元素表达式并详细推导了阻抗矩阵元素所涉及的各种积分运算的计算方法;通过数值计算实例与解析解或其它数值方法的详细对比分析,证明了计算公式的正确性.     

Analysis of transient scattering from composite arbitrarily shapedcomplex structures

A time-domain surface integral equation approach based on the electric field formulation is utilized to calculate the transient scattering from both conducting and dielectric bodies consisting of arbitrarily shaped complex structures. The solution method is based on the method of moments (MoM) and involves the modeling of an arbitrarily shaped structure in conjunction with the triangular patch basis functions. An implicit method is described to solve the coupled integral equations derived utilizing the equivalence principle directly in the time domain. The usual late-time instabilities associated with the time-domain integral equations are avoided by using an implicit scheme. Detailed mathematical steps are included along with representative numerical results     

A comparison of integral equations with unique solution in theresonance region for scattering by conducting bodies

A comparison of integral equations, for problems involving scattering by arbitrary-shape conducting bodies, having a unique solution in the resonance region is presented. The augmented electric and magnetic field integral equations and the combined field integral equation, in their exact and approximate versions, are considered. The integral equations and the basis and test functions used in the method of moments to solve them are reviewed. Their implementation in a computer code is analyzed, mainly the relation between the matrix properties and the CPU time and memory. Numerical results (condition number and backscattering cross section) are presented for the cube. It is shown that the combined field integral equation, and the approximate (symmetric) combined field integral equation, are the most efficient equations to use in the neighborhood of resonant frequencies, because the overdetermined augmented integral equations require an extra matrix multiplication     

An integral equation formulation of the direct scattering problem for an inhomogeneous slab

A numerical technique based on an integral equation scheme is developed for solving the direct scattering problem for an inhomogeneous slab. The integral equation is derived, using the induced current concept and the Green's function technique. The numerical method of solving the integral equation is presented. The method is proved to be numerically satisfactory and is applied to the slab of specific profiles. Numerical results for several cases are also included.     

位积分方程组矩量法用于精确计算非均匀介质柱的电磁散射

位积分方程组的主要特点是以电磁位为未知函数,这些未知函数在具有不同电磁参数的介质分界面处是连续的,因而在矩量法的实现过程中能够非常方便地应用高阶插值基函数来展开未知函数,以便获得高精度的解。但是,经典的点匹配方案使该模型的数值稳定性较差。本文用位积分方程组矩量法模型计算任意截面非均匀介质柱的电磁散射,采用三角形离散方案和高阶插值基函数,在测试过程中应用新提出的测试方法,克服了原位方程组矩量法模型的数值不稳定性。对矩量法矩阵中自阻抗元素的奇异性处理方法也作了详细介绍。文中提供的数值结果表明,该方法是精确、稳定的。     

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     

Adaptive multiscale moment method (AMMM) for analysis of scatteringfrom three-dimensional perfectly conducting structures

The adaptive multiscale moment method (AMMM) is presented for the analysis of scattering from three-dimensional (3D) perfectly conducting bodies. This algorithm employs the conventional moment method (MM) using the subsectional triangular patch basis functions and a special matrix transformation, which is derived from solving the Fredholm equation of the first kind by the multiscale technique. This methodology is more suitable for problems where the matrix solution time is much greater than the matrix fill time. The widely used triangular patch vector basis functions developed by Rao et al., (1982), are used for expansion and testing functions in the conventional MM. The objective here is to compress the unknowns in existing MM codes, which solves for the currents crossing the edges of the triangular patch basis functions. By use of a matrix transformation, the currents, source terms, and impedance matrix can be arranged in the form of different scales. From one scale to another scale, the initial guess for the solution can be predicted according to the properties of the multiscale technique. AMMM can reduce automatically the size of the linear equations so as to improve the efficiency of the conventional MM. The basic difference between this methodology and the other wavelet-based techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly in an iterative fashion even though it is an unknown. Two numerical results are presented, which demonstrate that the AMMM is a useful method for analysis of electromagnetic scattering from arbitrary shaped 3D perfectly conducting bodies     

An Efficient Volume Integral Equation Solution to EM Scattering by Complex Bodies With Inhomogeneous Bi-Isotropy

A generalized volume integral equation method is formulated for electromagnetic scattering by arbitrarily shaped complex bodies with inhomogeneous bi-isotropy. Based on the volume equivalence principle, the integral equations are represented in terms of a pair of coupled bi-isotropic polarized volume electric and magnetic flux densities. Reduction of the integral equations into the corresponding matrix equations is obtained using the method of moments (MoM) combined with the tetrahedral mesh. In the MoM solution, the three-dimensional solenoidal function is incorporated as the basis function defined over each tetrahedral element and the details of implementation, particularly the treatment of integral singularities, will be elucidated. The efficiency and accuracy of the proposed method are validated by illustratively supported examples.     

Direct extrapolation of a causal signal using low-frequency and early-time data

In this paper, we provide three direct procedures to extrapolate the early-time and the low-frequency response of a causal signal simultaneously in the time-and frequency domain. Compared with the extrapolation by orthonormal basis functions, direct extrapolation is straightforward and we do not need to evaluate the basis functions and search for the optimal scaling factor and the optimal number of basis functions. We show that the extrapolation introduced by Adve and Sarkar is equivalent to a Neumann-series solution of an integral equation of the second kind. It is further shown that this iterative Neumann expansion is an error-reducing method. We propose to solve this integral equation efficiently by employing a conjugate gradient iterative scheme. The convergence of this scheme is also demonstrated. We provide the matrix equations and show the equivalence to the integral equations, and demonstrate that the method of singular value decomposition (SVD) of solving the matrix equation provides accurate and stable results. Finally, a number of illustrative numerical examples are presented and the performances of the three direct methods are compared.     

Scattering analysis of a large body with deep cavities

A numerical scheme is presented for simulating electromagnetic scattering from a large and arbitrarily shaped body, coated with inhomogeneous composite materials, with large and deep cavities. This numerical scheme employs the higher order vector finite-element method (FEM) to discretize the fields inside the cavities and coatings and the higher order boundary integral (BI) method to terminate the FEM computational domain. A highly efficient special solver is designed to eliminate the unknowns inside the cavities, which yields a computed relation (CR) matrix over the cavity's aperture between the tangential electric and magnetic fields. This CR matrix is then combined with the finite element-boundary integral (FE-BI) matrix equation to form a complete linear system for the discrete fields everywhere in the computational domain. The resulting system is solved iteratively using a novel preconditioner derived by replacing the BI with a corresponding absorbing boundary condition (ABC).     

Electromagnetic scattering from composite objects using a mixtureof exact and impedance-boundary conditions

Different surface integral equations for characterizing the electromagnetic scattering from a surface impedance object partially coated with dielectric materials are presented. The impedance boundary condition (IBC) is applied on the impedance surface and the exact boundary condition is applied on the dielectric surface. The resulting integral equations are solved for bodies of revolution using the method of moments. The numerical results are compared with the exact solution for a sphere. Other geometries are considered, and their results are verified by comparing results of the numerical solutions which were obtained using different formulations. The internal resonance problem is examined. It is found that the combined field integral equation (CFIE) can be used at any frequency and with any surface impedance     

用MEI—FD方法分析Chiral媒质的电磁散射问题

本文应用不变性测试分程和有限差分方法分析Ｃｈｉｒａｌ媒质的电磁散射问题。应用该方法时，要在所讨论的区域内建立起一组有关电场和磁场的耦合差分方程，并且要在截断边界上应用不变性测试方程建立起有关边界点系数的方程。文中给出了一些非均匀、有耗且具有电大尺寸任意横截面Ｃｈｉｒａｌ柱的雷达散射截面的数值结果     

A Spectral Domain Integral Equation Method Utilizing Analytically Derived Characteristic Basis Functions for the Scattering From Large Faceted Objects

A novel technique, based on a spectral domain integral equation method with analytically derived characteristic basis functions, is introduced in this paper. It enables us to treat scattering problems from electrically large faceted bodies in a numerically rigorous and computationally efficient manner, in terms of both time and memory. The analytically derived characteristic basis functions include certain desirable features of the asymptotic schemes and are defined on subdomains that can be electrically large, not being bound to the typical discretization size of the conventional method of moments. By properly weighting through a Galerkin procedure the resulting electric field integral equation, the problem is reduced to a matrix equation having dimensions that do not depend on the size of the scatterer but only on its shape. Electrically large problems can be handled in a computationally efficient manner by using the proposed method since the associated matrix size is relatively small; moreover, all the reduced matrix elements are calculated in the spectral domain without evaluating any convolution products.     

Numerical solution of integral equations for dielectric objects ofprismatic shapes

A numerical method to investigate scattering from dielectric geometries of prismatic shapes has been developed. The surface integral equations are formulated by Schelkunoff's equivalence principle in terms of equivalent surface electric and magnetic currents. To solve these integral equations for the unknown currents, the object's cross-section is mapped onto a circle. In the transformed space, Fourier type entire-domain basis functions are used in the cross section and triangular subdomain basis functions are selected along the generating curve to represent the currents. A moment method is then used to reduce the integral equations to a matrix equation to compute the current coefficients. It is found that the transformation of the object's surface to a circular shape improves the convergence of the current mode in the cross-section. However, the current modes are coupled on the surface and the matrix equation includes all the modes     

Scattering by Conducting Bodies Coated With Bi-Isotropic Materials

Electromagnetic scattering by arbitrarily shaped conducting bodies coated with general bi-isotropic materials is formulated in terms of the surface integral equation method. In order to facilitate the implementation of the surface equivalence principle, a field decomposition scheme is utilized to split a bi-isotropic media into two equivalent isotropic media. By enforcing the boundary condition on the interfaces of the body, a set of coupled integral equations is finally obtained for the unknown surface currents and then numerically solved using the moment methods combined with the vector triangular basis function. The fast multipole technique has been embedded into the algorithm to accelerate the solution process. The validity of theoretical formulations is verified by numerical results and their comparisons. The calculated results for bi-isotropically coated conducting spheres and oblate spheroids are compared with the exact solution and the existing data, and excellent agreements are observed.     

A hybrid equation approach for the solution of electromagneticscattering problems involving two-dimensional inhomogeneous dielectriccylinders

A numerical procedure for the solution of electromagnetic scattering problems involving inhomogeneous dielectric cylinders of arbitrary cross section is discussed. The cases of illumination by both transverse magnetic (TM) and transverse electric (TE) plane waves are considered. The scattering problems are modeled via a hybrid integral-equation/partial-differential-equation approach. The method of moments is applied to obtain a system of simultaneous equations that can be solved for the unknown surface current densities and the interior electric field. The interior region partial differential equation and the exterior region surface integral equation are coupled in such a manner that many existing surface integral equation computer codes for treating problems involving scattering by homogeneous dielectric cylinders can be modified easily to generate the block of the matrix corresponding to the surface current interactions. The overall system matrix obtained using the method of moments is largely sparse. Numerical results are presented and compared with exact solutions for homogeneous and inhomogeneous circular cylinders     

粗糙面与目标电磁散射统计特性分析

首先给出用于描述和产生粗糙海面的模型，然后在锥形平面波入射条件下，用矩量法求解了粗糙面及与圆柱形近地小目标复合散射所满足的积分方程，最后给出了不同条件下粗糙面、粗糙面与目标复合散射特性的统计结果及相互间的比较。     

The Solution of Waveguide Scattering Problems by Application of an Extended Huygens Formulation

The implementation of a recent new hybrid integral-equation/vector finite-element method formulation applicable to inhomogeneous obstacle scattering in hollow waveguide, requiring discretization just of the obstacle, is presented. The integral equation links the given incident modes with the discontinuity-surface electric and magnetic fields. The finite-element equation is expressed in terms of the entire magnetic and surface electric field of the obstacle. Compatible vector finite-element basis function expansions are inserted, resulting in a pair of matrix equations soluble for the unknown electric and magnetic basis coefficients. Corresponding two-port scattering parameters are further derived. Test cases of posts in the$ TE_10$waveguide, with details of the matrix constructions, are described. Numerical results verified against an established commercial code are given. The ability to model inhomogeneous, lossy, and multiple scatterers is demonstrated.     

Electromagnetic scattering from a chiral cylinder-general case

A generalized finite-difference (FD) scheme combined with the measured equation of invariance (MEI) is presented for the analysis of electromagnetic scattering from an inhomogeneous and lossy chiral cylinder with electrically large, arbitrarily shaped cross section. A new FD mesh in both chiral and achiral regions is formed, and the FD equations in a chiral medium are derived; then a large sparse matrix is formulated. The numerical results of bistatic scattering width (two-dimensional radar cross section) are given for the chiral cylinders of rectangular, elliptical, and complex cross section, respectively. Some results are compared with available data