Comparison of Integral-Equation Formulations for the Fast and Accurate Solution of Scattering Problems Involving Dielectric Objects with the Multilevel Fast Multipole Algorithm

We consider fast and accurate solutions of scattering problems involving increasingly large dielectric objects formulated by surface integral equations. We compare various formulations when the objects are discretized with Rao-Wilton-Glisson functions, and the resulting matrix equations are solved iteratively by employing the multilevel fast multipole algorithm (MLFMA). For large problems, we show that a combined-field formulation, namely, the electric and magnetic current combined-field integral equation (JMCFIE), requires fewer iterations than other formulations within the context of MLFMA. In addition to its efficiency, JMCFIE is also more accurate than the normal formulations and becomes preferable, especially when the problems cannot be solved easily with the tangential formulations.      

Efficient Two-Dimensional Extrapolation Technique of Scattering Problems Involving Dielectric Objects Using PMCHWT Formulation

An efficient extrapolation technique of Radar cross-section （RCS） combines with Poggio-Miller- Chang-Harrington-Wu-Tsai （PMCHWT） formulation is presented for the fast analysis by arbitrary shaped three- dimensional homogeneous lossy dielectric objects. The PMCHWT formulation obtained in a well-known manner is discretized to matrix equations using the Method of moments （MoM）. For the RCS is highly angular dependent as well as frequency, a novel rational function scheme is extended to the induced currents associated with PMCHWT, which can provide fast and accurate radar cross-section computation in both the frequency domain and spatial domain simultaneously. Numerical results are presented for two canonical dielectric scatterers.     

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     

E-P-AMCBFM分析介质与PEC混合体的电磁散射

使用基于表面积分方程的矩量法来分析介质与理想导体混合体的电磁散射是计算电磁学的一大热点。对理想导体目标体表面建立电场积分方程,在介质目标体表面建立PMCHW方程组,与基于矩阵分块技术的自适应修正特征基函数法结合,对介质涂敷理想导体目标体的电磁散射进行分析,将其称之为EFIE-PMCHW-AMCBFM(E-P-AMCBFM)。并讨论不同参数如基函数阶数,矩阵块间重叠区域等对计算效率的影响,数值结果表明E-P-AMCBFM对于处理介质-理想导体混合体的电磁散射问题具有较高的精度和效率。     

An Accurate Solution of the Cylindrical Dielectric Resonator Problem

A cylindrical sample of low-loss high-epsilon/sub r/, dielectric placed between two parallel conducting plates perpendicular to the sample axis forms a microwave resonator. A new method of determining the field distribution and resonant frequency of this resonator is presented. By this method the solution is obtained in a form of successive approximations converging to the exact solution. The analysis is outlined in detail for the TE/sub 01delta/ mode and compared with previously published approximate calculations and experimental data.     

Calculations of Infrared Laser Beam Scattering from Rough Dielectric Objects

The coherent and incoherent scattering cross sections of Infrared Laser Gaussian beam scattering from arbitrarily shaped convex dielectric objects with rough surfaces are investigated by using plane wave spectrum method and physical optics approximation. In the paper, the infrared laser scattering cross sections of rough sphere are calculated at 10.6 μm , and the influence of the beam size, permittivity, and polarization as well as roughness parameters is analyzed numerically. When the beam size is much larger than the size of object, the results in the paper can reduce to those of an incident plane wave. On the other hand, for the case of roughness statistical parameter close to zero, only the forward scattering has a parent difference compared with the result of gaussian beam scattering from smooth sphere.     

三维目标电磁散射矢量有限元/边界元法的公式研究

研究应用于三维目标电磁散射分析的矢量有限元/边界元混合方法不同公式.分析表明,混合公式系统矩阵的条件数随边界元采用不同公式有很大差异,从而导致混合公式的稳定性有很大不同.并讨论了混合方法中边界元部分的单一检验基函数方法和组合检验基函数方法.认为组合检验基函数方法仍可被视为单一检验基函数方法;通过比较边界元部分使用单一检验基函数法和组合检验基函数法时所得计算结果,纠正了只有使用组合检验基函数,有限元/边界元混合方法才能得到精确结果的结论.综合考虑计算结果可靠性、精度及对内部谐振的免疫力等因素,给出了所推荐使用的有限元/边界元混合方法公式.     

用时域积分方程法计算介质目标的电磁散射

本文应用时域积分方程法计算介质目标的散射场，并以球体和带球帽的圆柱体为例给出了沿轴向入射平面波的电磁散射结果，与实际测试结果非常一致，值得指出的是，虽然本文给出的介质目标具有平面对称性，但该方法适用于任意形状的目标。     

金属-介质混合目标电磁散射的P-FFT快速求解

针对任意形状金属-介质混合目标的电磁散射问题,使用矩量法将体-面结合的积分方程(VSIE)转换成线性方程组,并利用预修正快速傅立叶变换(P-FFT)方法来进行快速求解.为减少直接计算和预修正的近区未知量个数,采用一种改进的模板拓扑.数值计算结果表明,基于VSIE的P-FFT方法可以高效准确地求解金属-介质混合目标的电磁散射问题,改进的模板拓扑可以显著减少近区未知量个数,从而减少算法的存储需求和计算时间.     

A Least-Squares Boundary Residual Method for the Numerical Solution of Scattering Problems

An explicit least-squares criterion is put forward as an alternative to the point-matching method of numerically solving scattering problems. While being an established method of functional approximation, it has been largely ignored in numerical approaches to electromagnetic scattering. In contrast to point matching, the least-squares approach has a rigorous proof of convergence. An electric/magnetic weighting factor is found useful in optmizing convergence. Finally, it allows use of perhaps the fastest and most compact matrix inversion algorithm.     

Accurate Solution of Microstrip and Coplanar Structures for Dispersion and for Dielectric and Conductor Losses

For the analysis of coplanar- and microstrip-type structures, a higher order solution of the spectral-domain approach is introduced. Legendre polynomials are used as the basis functions for fields having singularities near the edges, leading to fast convergence to the exact solution. A perturbation technique is combined with the spectral-domain method to evaluate conductor and dielectric losses in microstrip, inverted microstrip, and coupled microstrip in the metallic enclosure. Computations of characteristic impedance and losses incurred in several structures are also presented. Central processing unit (CPU) time on an IBM 360/65 for the zeroth-order approximation ranges from 1 to about 5 s for the whole computation, and increases if higher order of solution is requested for better accuracy. The calculation of attenuation due to conductor losses is found to be particularly sensitive to order of approximation, so that the generally used "zeroth-order" solution is inadequate. A user-oriented program package has been written, including options on order of mode, order of solution (i.e., of approximation), impedance, attenuation, and number of substrates. Although written for single or coupled microstrip, the program can be adapted for arbitrary arrangements of thin coplanar conductors. The program is described separately.     

封闭介质盒中三维隐藏金属目标的散射仿真和图像重构

基于点目标散射原理,通过计算封闭介质中隐藏目标的全方位电磁散射,进行成像重构.宽带频率步进雷达从不同水平方位发送平面电磁波探测隐藏目标,获取隐藏目标各水平方位向后向散射电场.通过二维样条插值得到二维均匀采样的散射电场,将重采样数据进行二维快速Fourier变换得到二维重构图像.采用体面混合积分方程的矩量法计算复杂结构金属目标与介质盒环境的后向散射电场.通过有、无隐藏目标时的多方位后向散射电场的差值场实现目标重构成像.由封闭介质盒中隐藏3个金属球和1把金属手枪,分别进行重构成像,以说明该方法的有效性.     

TD‐CFIE Formulation for Transient Electromagnetic Scattering from 3‐D Dielectric Objects

In this paper, we present a time domain combined field integral equation formulation (TD‐CFIE) to analyze the transient electromagnetic response from dielectric objects. The solution method is based on the method of moments which involves separate spatial and temporal testing procedures. A set of the RWG functions is used for spatial expansion of the equivalent electric and magnetic current densities, and a combination of RWG and its orthogonal component is used for spatial testing. The time domain unknowns are approximated by a set of orthonormal basis functions derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable makes it possible to handle the time derivative terms in the integral equation and decouples the space‐time continuum in an analytic fashion. Numerical results computed by the proposed formulation are compared with the solutions of the frequency domain combined field integral equation.     

Application of the Rotating Angle Parabolic Equation Method for the Solution of Scattering Problems

In this paper the rotating angle parabolic equation method (PEM) is presented for the solution of scattering problems. Separate spectral domains for the incident and scattered fields are obtained and their sum is substituted into the wave equation. Considering the satisfaction of wave equation by the incident and scattered fields, the solution of wave equation changes into the solution of two separate parabolic equations for the incident and scattered fields. The paper continues with the development of an algorithm for the determination of back scattered fields from knife edges and scattered fields from the slope and slope discontinuities. It will be seen that the results of the proposed algorithm agree with those of other methods for the solution of aforementioned problems.

Integral-Equation Analysis of 3-D Metallic Objects Arranged in 2-D Lattices Using the Ewald Transformation

We present a space-domain integral-equation method for the analysis of periodic structures formed by three-dimensional (3-D) metallic objects arranged in a general skewed two-dimensional lattice. The computation of the space-domain Green's function is accelerated using the Ewald transformation. The method is validated on several periodic structures ranging from planar frequency-selective surfaces to 3-D photonic crystals and metamaterials. For these structures, our technique shows a clear advantage in terms of computational speed when compared with available commercial softwares.     

On the Scattering of Electromagnetic Waves by Periodic Rough Dielectric Surfaces: A BOA Solution

A new approach for the scattering of electromagnetic (EM) waves from periodic dielectric rough surfaces is addressed. The method is an extension of the buried object approach (BOA), which is developed for rough surfaces of infinite extend, to the present problem. The BOA allows to model the original problem as the scattering of EM waves from cylindrical objects located in a two-half-space medium with planar interface. Then, the problem is reduced to the solution of a Fredholm integral equation of second kind through the periodic Green's function of two-half-space medium. The periodic Green's function of two-half-space medium is calculated via the Floquet mode expansion, whose numerical evaluation can be accelerated by using effective methods. The method can also be used to solve the scattering problems of rough surfaces of infinite extend and having a localized roughness. Numerical simulations show that the method yields effective and accurate results for surfaces of arbitrary variation.      

Numerical Solution of Waveguide Scattering Problems by Finite-Difference Green's Functions

A finite-difference Green's function method for solving time-harmonic wave guide scattering problems involving metallic obstacles of finite size by computer is described. The method is applied to the two-dimensional problem of a TE/sub 10/ mode impinging on cylindrical metallic posts of arbitrary shape in a rectangular waveguide. The equivalent susceptance of a transverse semidiaphragm computed using a 50 point approximation for the induced current distribution is found to be 1.5 percent less than the exact value. The S matrix of a thin bent window versus wavelength is also presented.     

任意截面导体柱的电磁散射数值解

卡门翼形和任意多边形是两种典型的不规则形体，由于其不规则曲边和尖锐的角点，它们的电磁散射问题给传统的FDTD数值求解造成了一定的困难，这是因为要获得较高的精度，必须细分网格，从而增加内存需求和计算时间，本文利用形体变换结合时域有限差分法的Thompson-FDTD方法对这两种典型的不利形体的散射问题进行了数值模拟，其结果进一步验证了Thompson-FDTD方法对散射体几何形状变化具有较强的适应能力和较高的数值精度。     

Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell's Equations

A numerical method is described for the solution of the electromagnetic fields within an arbitrary dielectric scatterer of the order of one wavelength in diameter. The method treats the irradiation of the scatterer as an initial value problem. At t = 0, a plane-wave source of frequency f is assumed to be turned on. The diffraction of waves from this source is modeled by repeatedly solving a finite-difference analog of the time-dependent Maxwell's equations. Time stepping is continued until sinusoidual steady-state field values are observed at all points within the scatterer. The envelope of the standing wave is taken as the steady-state scattered field. As an example of this method, the computed results for a dielectric cylinder scatterer are presented. An error of less than /spl plusmn/10 percent in locating and evaluating the standing-wave peaks within the cylinder is achieved for a program execution time of 1 min. The extension of this method to the solution of the fields within three-dimensional dielectric scatterers is outlined.