A coupled surface-volume integral equation approach for thecalculation of electromagnetic scattering from composite metallic andmaterial targets

A coupled surface-volume integral equation approach is presented fur the calculation of electromagnetic scattering from conducting objects coated with materials. Free-space Green's function is used in the formulation of both integral equations. In the method of moments (MoM) solution to the integral equations, the target is discretized using triangular patches for conducting surfaces and tetrahedral cells for dielectric volume. General roof-top basis functions are used to expand the surface and volume currents, respectively. This approach is applicable to inhomogeneous material coating, and, because of the use of free-space Green's function, it can be easily accelerated using fast solvers such as the multilevel fast multipole algorithm     

Evaluation of LEMP effects on complex wire structures located abovea perfectly conducting ground using electric field integral equation intime domain

In this paper, a novel approach for the implementation of scattering theory is proposed in order to evaluate the electromagnetic effects of lightning return stroke on complex wire structures (lightning EM pulse - LEMP). An electric field integral equation (EFIE) in the time domain is employed to describe the electromagnetic transients from lightning. The proposed approach is applied to a single-phase, three-phase as well as a Y-shaped transmission line located above a perfectly conducting ground. The simulation results reproduce accurately experimental data available in the literature. The proposed method provides new possibilities in estimation of lightning indirect effects on complex networks as an example “radial transmission systems tapped from main switching substations” are investigated     

Broadband Müller-MLFMA for Electromagnetic Scattering by Dielectric Objects

The multilevel fast multipole algorithm (MLFMA) is very efficient for solving large-scale electromagnetic scattering problems. However, at low frequencies, or when the discretization is small compared with the wavelength, both the MLFMA and the underlying integral equation formulation typically suffer from a subwavelength breakdown. For the electromagnetic scattering from a homogeneous dielectric object, we obtain a stable and well-conditioned surface integral formulation using a variant of the classical Muumlller formulation and linear basis functions. To overcome the subwavelength breakdown of the MLFMA, we use both propagating and evanescent plane waves to represent the fields. The implementation is based on a combination of the spectral representation of the Green's function and Rokhlin's translation formula. We also present a new interpolation scheme for the evanescent part, which significantly improves the error-controllability of the MLFMA-implementation. Several numerical results verify both the error-controllability and scalability of the proposed algorithm     

MOM/Lanczos-AWE算法快速求解良导体柱的RCS宽带与宽角响应

考虑导体柱的电磁散射 ,由于一般实际导体为良导体 ,若利用表面阻抗的边界条件 ,则良导体柱的电场积分方程 (EFIE)为第二类Fredholm积分方程 ;将矩量法 (MOM )应用到该积分方程时 ,该积分方程转化为第二类Fredholm矩阵方程。本文提出了一种求解第二类Fredholm矩阵方程的Lanczos AWE递归迭代快速算法 ,首先采用Lanczos技术快速求解在某一给定频率或角度时第二类Fredholm矩阵方程 ,得到在该频率或角度时良导体的表面电流分布 ;然后采用渐近波形估计 (AWE)技术求取所考虑的频段内任意频率或角度范围内任意角度时良导体的表面电流分布。根据表面电流分布预测了任意形状良导体柱的单站雷达散射截面 (RCS)的宽带与宽角响应。计算结果表明Lanczos AWE技术可大大加快MOM法的计算速度。     

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。     

基于EM算法的宽带信号DOA估计及盲分离

本文提出了一种基于EM算法的宽带信号DOA估计与盲分离方法.首先将宽带混合信号转换到频域,然后综合利用带宽内所有频点信息建立似然函数,在此基础上推导出宽带条件下的EM迭代式,从而实现宽带信号DOA及波形的联合估计.并且本文通过分析EM算法的收敛性,自适应的设定角度搜索空间,提高了算法的运算效率.与传统方法相比,本文方法运用的有效信息更多,因此,其在DOA估计精度及波形恢复性能方面都更有优势.仿真实验表明了该算法的有效性.     

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     

An IE-ODDM-MLFMA Scheme With DILU Preconditioner for Analysis of Electromagnetic Scattering From Large Complex Objects

For electrically large complex electromagnetic (EM) scattering problems, huge memory is often required for most EM solvers, which is too difficult to be handled by a personal computer (PC) even a workstation. Although the multilevel fast multipole algorithm (MLFMA) effectively deals with electrically large problems to some extent, it is still time and memory consuming for very large objects. In order to further reduce the CPU time and the memory requirement, a hybrid algorithm, based on the overlapped domain decomposition method for integral equations (IE-ODDM), MLFMA and block-diagonal, incomplete lower and upper triangular matrices (DILU) preconditioner, is proposed for the analysis of electrically large problems. The dominant memory requirement for plane wave expansions in the three processes of aggregation, translation and disaggregation in the MLFMA is drastically reduced by the first two techniques. The iterative procedure for each overlapped subdomain solved by the MLFMA is effectively sped up by the DILU preconditioner. After integrating these techniques, the proposed hybrid algorithm is more efficient in computing time and memory requirement compared to the conventional MLFMA and is more suitable for analyzing very large EM scattering problems. Enough accurate solution can be obtained within quite a few outer iterations, where an outer iteration means a complete sweep for all the subdomains. Some numerical examples are presented to demonstrate its validity and efficiency.     

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。     

应用互耦迭代法计算二维随机海面微波散射

海面对微波散射可用介质散射PMCHW方程描述,针对其离散后阻抗矩阵块的特点,引入电磁互耦迭代方法,结合多层快速多极子(MLFMA)求解,给出计算海面散射等效电流源和磁流源的算法.使用该方法求解分析得到不同起伏程度的海面对微波散射方向性的影响及规律,所得到的规律与文献报道实验测试结论相比较,对比结果验证方法的正确性.     

An efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures

An efficient multilevel fast multipole algorithm (MLFMA) formalism to model radiation and scattering by/from large planar microwave structures is presented. The technique relies on an electric field integral equation (EFIE) formulation and a series expansion for the Green dyadic, based on the use of perfectly matched layers (PML). In this way, a new PML-MLFMA is developed to efficiently evaluate matrix-vector multiplications arising in the iterative solution of the scattering problem. The computational complexity of the new algorithm scales down to O(N) for electrically large structures. The theory is validated by means of several illustrative, numerical examples.     

Adaptive zero-tracking complemented by LMS weight update forguaranteed convergence

A low-complexity zero-tracking algorithm with fast and guaranteed convergence behavior is proposed and investigated. The algorithm implements a zero-tracking algorithm and a least mean square (LMS) weight update algorithm in parallel, with the former adjusting the zeros of the array in a time-multiplexed manner to achieve fast asymptotic and tracking behavior, while the latter improves the initial transient behavior of the algorithm and guarantees its convergence to the global optimum. By comparing their output powers, the relative performances of the two component algorithms are monitored, and re-initialization of one algorithm by the other may occur periodically. This gives the algorithm both fast and guaranteed convergence behavior, even though the zeros are directly available and the implementation complexity is only two times that for the conventional LMS algorithm     

Broadband Beamforming Using TDL-Form IIR Filters

Conventional broadband beamforming structures make use of finite-impulse-response (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signal-to-interference-plus-noise-ratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequency-dependent array weighting of broadband beamformers could be better approximated by infinite-impulse-response (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frost-based and generalized sidelobe canceller (GSC)-based broadband beamformers utilizing a kind of tapped-delay-line-form (TDL-form) IIR filters are proposed; 2) the combined recursive Gauss-Newton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frost-based implementation; and 3) in the GSC-based structure, the unconstrained RGN algorithm is customized for the TDL-form IIR filters in the adaptive beamforming part. Compared with the beamformer using direct-form IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved     

Comparison of fast integral mesh truncation schemes for hybridFE-BI systems

By virtue of their low operation count, the application of fast integral methods such as the fast multipole (FMM) and adaptive integral methods (AIM) result in a substantial quickening of the boundary integral portion of the hybrid finite element-boundary integral (FE-BI) method, independent of the shape of the BI contour. Recently, various versions of the FMM have been proposed, each introducing a different approximation to the implementation of the boundary integral. The main goal of this Letter is to provide a comparison of the effect of these fast integral algorithms on the boundary integral when used in conjunction with the traditional FE-BI method     

The three-dimensional algorithm of solving the electric fieldintegral equation using face-centered node points, conjugate gradientmethod, and FFT

It has been known for a long time that the accuracy of solving the scattering by a dielectric body using the electric field integral equation (EFIE) is poor when the permittivity of the scatterer becomes large. Recently, this problem has been settled by using a procedure involving face-centered node points. Such a procedure is efficient, since it preserves the convolution property in the EFIE and, hence, the applicability of the fast Fourier transform (FFT). This procedure is generalized to the three-dimensional and anisotropic case. The generalization is quite straightforward in both the formulation and the programming. A calculation for a scatterer with a relative permittivity as high as 100 indicates that the proposed procedure converges quite rapidly, whereas the conventional using the conjugate gradient method approach fails to converge     

A single-level low rank IE-QR algorithm for PEC scattering problems using EFIE formulation

This paper presents a single-level matrix compression algorithm, termed IE-QR, based on a low-rank approximation to speed up the electric field integral equation (EFIE) formulation. It is shown, with the number of groups chosen to be proportional to N/sup 1/2/, where N is the number of unknowns, the memory and CPU time for the resulting algorithm are both O(N/sup 1.5/). The unique features of the algorithm are: a. The IE-QR algorithm is based on the near-rank-deficiency property for well-separated groups. This near-rank-deficiency assumption holds true for many integral equation methods such as Laplacian, radiation, and scattering problems in electromagnetics (EM). The same algorithm can be adapted to other applications outside EM with few or no modifications; and, b. The rank estimation is achieved by a dual-rank process, which ranks the transmitting and receiving groups, respectively. Thus, the IE-QR algorithm can achieve matrix compression without assembling the entire system matrix. Also, a "geometric-neighboring" preconditioner is presented in this paper. This "geometric-neighboring" preconditioner when used in conjunction with GMRES is proven to be both efficient and effective for solving the compressed matrix equations.     

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.     

Fast Full-Wave Surface Integral Equation Solver for Multiscale Structure Modeling

We describe a full-wave solver to model large-scale and complex multiscale structures. It uses the augmented electric field integral equation (A-EFIE), which includes both the charge and the current as unknowns to avoid the imbalance between the vector potential and the scalar potential in the conventional EFIE. The formulation proves to be stable in the low-frequency regime with the appropriate frequency scaling and the enforcement of charge neutrality. To conquer large-scale and complex problems, we solve the equation using iterative methods, design an efficient constraint preconditioning, and employ the mixed-form fast multipole algorithm (FMA) to accelerate the matrix-vector product. Numerical tests on various examples show high accuracy and fast convergence. At last, complex interconnect and packaging problems with over one million integral equation unknowns can be solved without the help of a parallel computer.      

Cramer–Rao Bound for MIMO Radar Target Localization With Phase Errors

A new template matching method accelerated by an integral image is proposed. In contrast to the conventional winner-update template matching algorithm, the proposed scheme uses an integral image instead of a block sum pyramid to represent the search area. When an integral image is used, block sums on the lowest level are evaluated very fast. As a result, the speed with which nonbest candidates are rejected is nearly double that of the conventional scheme. Moreover, the proposed scheme needs less memory than the conventional approach to maintain block sums of candidates and can be easily extended to nonsquare (rectanglar) template matching.      

A higher order FDTD method in Integral formulation

We present a fourth-order (4, 4) finite-difference time-domain (FDTD)-like algorithm based on the integral form of Maxwell's equations. The algorithm, which is called the integro-difference time-domain (IDTD) method, achieves its fourth-order accuracy in space and time by taking into account the spatial and temporal variations of electromagnetic fields within each computational cell. In the algorithm, the electromagnetic fields within each cell are represented by space and time integrals (or integral averages) of the fields, i.e., the electric and magnetic fluxes (D,B) are represented by the surface-integral average, and the electric and magnetic fields (E,H) by the line and time integral average. In order to relate the integral average fields in the staggered update equations, we have obtained constitutive relations for these fields. It is shown that the IDTD update equations combined with the constitutive relations are fourth-order accurate both in space and time. The fourth-order correction terms are represented by the modified coefficients in the update equations; the numerical structure remains the same as the conventional second-order update equations and more importantly does not require the storage of field variables at the previous time steps to obtain the fourth-order accuracy in time. Furthermore, the Courant-Friedrichs-Lewy (CFL) stability criteria of this fourth-order algorithm turns out to be identical to the stability limits of conventional second-order FDTD scheme based on differential formulation.