EM Programmer's Notebook [EM scattering]

An interactive circular-cylinder modeler software program in which the approximation of a complex scatterer is achieved by using circular cylinders is described. The cylinders are made of either homogeneous isotropic dielectric material, perfectly conducting material characterized by a surface impedance, or a combination of the two. The user interface is designed for quick construction of two-dimensional scatterers using circular cylinders of arbitrary radii. The algorithm for multiple scattering between these cylinders is based on the enforcement of the appropriate boundary conditions on the surface of each cylinder. The source of excitation can be a plane wave or a line source parallel to the scatterer, and both TM and TE types of polarization are considered     

Implementation and application of resistive sheet boundarycondition in the finite-difference time-domain method [EM scattering]

Use of a resistive sheet boundary condition in the finite-difference-time-domain (FDTD) analysis of scattering problems involving a resistively coated dielectric object is described. An algorithm is introduced through an analysis of E-polarized scattering from a thin resistive strip. For a given resistance, numerical experiments indicate that algorithm stability is ensured for time sampling intervals chosen according to a specific criterion. Validity of the resultant FDTD method is verified in a comparison of computed E-polarized scattering data for several resistive strips with existing data. Results on the E-polarized scattering behaviour of a resistively coated dielectric strip as a function of surface resistances and angle of incidence are also presented. Extension to the H-polarized case and application of the present method to pulsed problems are briefly discussed     

Low frequency scattering by a resistive plate

For a plane wave incident on a resistive plate, the first two terms in the low frequency expansion of the far field are determined. Since the magnetic dipole is not excited if the resistivity is nonzero, the leading term is simply the electric dipole contribution, and is identical to that for a perfectly conducting plate. The resistivity appears explicitly in the next term which can be expressed in terms of potentials. Some implications of the results are discussed, and the method is illustrated in the case of a circular disk.     

FDTD algorithm in curvilinear coordinates [EM scattering]

The finite-difference-time-domain (FDTD) algorithm for the solution of electromagnetic scattering problems is formulated in generalized coordinates in two dimensions and implemented in a code with the lowest-order Bayliss-Turkel radiation boundary condition expressed in cylindrical coordinates. It is shown that, for a perfect conductor, such a formulation leads to a stable, well-posed algorithm and that, in regions where the curvature of the coordinate lines is not great, the dispersion and anisotropy effects are negligible. Such effects become more pronounced in regions of high curvature, leading to unphysical phase shifts. The magnitude of such shifts and the amount of wavefront distortion is studied via numerical experiments using a cylindrical mesh. Near-field results are given for two canonical shapes for each polarization: the circular cylinder and cylinders of square and rectangular cross sections. These results are compared with those obtained by exact eigenfunction expansion techniques, with method-of-moments (MM) solutions, and with solutions obtained from an alternate FDTD approach. In each case, agreement is excellent. The propagation of a plane wave through a polar space in the absence of a scatterer is also examined, and it is shown that the FDTD algorithm is capable of tracking the incident wave closely     

A unified theory of thin material wires [EM scattering]

The author presents an integral equation and method of moments (MM) solution to the problem of scattering by a thin material wire of circular cross section. In general the material wire has permittivity and permeability different from those of free space. The wire of radius a must be sufficiently thin so that k₀a ≪1, where k₀ is the free space wavenumber. However, there is no restriction on |k|a, where k is the wavenumber in the material wire. The method is referred to as unified in that it applies to thin material wires of arbitrary complex permittivity and permeability. Thus, a single or unified formulation applies to a low-density dielectric/ferrite wire or to a highly conducting metallic wire     

An algorithm to implement a surface impedance boundary conditionfor FDTD [EM scattering]

Two models for numerically simulating a surface impedance boundary condition in FDTD are presented. The resulting algorithm is easy to implement, requiring only trivial modification to a code written for a perfect electrical conductor boundary condition     

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 entire-domain basis functions with square-root edge singularity[EM scattering]

The surface current density generated on thin conducting scatterers or radiations has a well-known singular edge behaviour. Using an explicit transformation between certain regular and singular basis functions, the author compares the convergences of the current expansions of both sets. Also studied are the complementary expansions of the scattered field which result from integrating the current. The discussion is extended to periodic strip structures where the phenomenon of relative convergence is demonstrated     

Determination of the natural modes for a rectangular plate[transient scattering]

A coupled surface integral equation formulation for determination of the natural frequencies of a rectangular plate is proposed. The method of moments solution to this formulation and the subsequent numerical results are presented. The natural frequencies predicted by the theory have been verified by an experiment. In comparison with the existing formulation of this problem, the present formulation predicts equally well for the first few dominant modes but better for the higher modes. Also, in the present formulation, no convergence problem has been encountered     

Solution stability of iterative schemes utilizing the discreteFourier transform [EM scattering]

The Fredholm integral equation of the first kind can be solved numerically using iterative schemes which minimize the integral square error. When the kernal is of the convolution type, the discrete Fourier transform (DFT) can be used when evaluating the operator equation in the iterative schemes. However, the DFT imposes an artificial periodicity, thus changing the nature of the problem. The effect of this on the solution has been studied and convergence investigated by comparison with a method of moments solution. A proposed method of avoiding the periodicity problem has been studied. The effect of introducing losses in the medium surrounding the scatterer has been investigated; provided losses are low, there is little effect on the solution     

Radiation and low-frequency scattering of EM waves in a generalanisotropic homogeneous medium

This paper focuses on a boundless homogeneous medium with general anisotropy of electromagnetic properties. The explicit exact form of the four spectral Green's dyads Gˆ_νξ(k) is obtained and a coordinate-free representation of the four spatial Green's functions Gˆ_νξ(x-x') in terms of one scalar potential W(x-x') is developed. On this basis, asymptotic expressions for the radiation field due to arbitrary sources are derived that show that the associated modes and the eigenmodes determine radiation along a singular optic axis and in all other directions, respectively. Using an integral equation approach and the theory of Newtonian potential, the problem of low-frequency scattering by a small anisotropic ellipsoidal body immersed into an anisotropic medium is solved analytically     

Note on interpolational basis functions in the method of moments[EM scattering]

Efficient basis sets for the method of moments may be obtained using quasi-localized bandlimited interpolational functions that, broadly speaking, are defined relative to a mean sampling rate that is adjusted to curvature and proximity to edges, thus reflecting the local spatial-frequency bandwidth. Computed scattering data in a number of structures, including perfectly conducting circular and elliptical two-dimensional cylinders as well as a flat infinite strip, indicate that reasonable accuracy can be obtained with an average rate of between 2.5 and 3 basis functions per wavelength. Average sampling rates need not correspond strictly to the bandwidth of the basis functions, and there is considerable latitude with respect to random variation of sampling intervals. Although each basis function typically extends over several sample points, required integrals can be obtained speedily by the use of standard sampling-theoretical methods     

Application of the discrete Fourier transform method to thindielectric structures [EM scattering]

The discrete Fourier transform method is a numerical technique designed to take advantage of the convolution structure that often appears in the differential-integral equations arising from electromagnetic scattering. It used the fast Fourier transform (FFT) to compute both the derivatives and the convolution integrals. As a consequence, this method is easy to program, uses less computer memory than comparable methods, yields accurate predictions, and in general, offers a better rate of convergence. This technique, which is particularly suited for solving problems where the scatterer is made of a dielectric material and has a shape which can be approximated accurately by a rectangular grid, is applied to thin dielectric slabs with both electric and magnetic properties. It is shown that by choosing the conductivity sufficiently large, a thin dielectric slab behaves like a metallic plate. On the other hand, with a suitable choice of conductivity, a particular thin dielectric slab will act like a resistive plate     

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     

圆柱导体电磁散射问题分析

利用矩量法对圆柱导体电磁散射特性进行了研究.基于伽略金法,采用分域基函数展开模式,得出了圆柱导体的电磁散射方向图,并对圆柱体直径和入射波波长不同比例情况下的散射情况进行了研究.文中还用MATLAB给出了圆柱体电磁散射的精确计算结果.     

平行板电容器中介质受力问题的讨论

用虚功原理计算介质块在平行板电容器中的受力,是一道经典电磁场例题。在忽略边缘效应的情况下,垂直方向的电场如何产生了一个横向的作用力？本文回顾和分析了历史上的一些讨论,明确了边缘场对介质中电偶极矩的作用是介质受到横向力的根本原因,解释了为什么使用虚功原理可以忽略边缘效应,讨论了介质分界面的受力问题,澄清了一些错误的认识。     

Error analysis for the truncation of multipole expansion of vectorGreen's functions [EM scattering]

One of the most important mathematical formulas in fast multipole algorithms (FMA) is the addition theorem. In the numerical implementation of the addition theorem, the infinite series should be truncated. In this paper, the number of terms needed for the scalar Green's function is derived, and the error analysis for the truncation error in the multipole expansion of the vector Green's functions is given. We have found that the error term in vector Green's functions is proportional to 1/R. If the scalar Green's function is truncated at the L-th term and the relative error is ϵ, then the relative error in the dyadic Green's function is ϵ/4, if it is truncated at the (L+2)-th term. For the vector Green's function related to MFIE, the relative error is ϵ/2 if it is truncated at the (L+1)-th term     

Convergence criteria for the extended matrix version of thespectral iteration technique [EM scattering]

An extended matrix version of the spectral iteration technique (SIT) has been reported recently, where it was shown to offer the possibility of significantly improving the convergence rate for homogeneous dielectric or conducting scatterers by introducing a taper. It is shown that there are good grounds for introducing such a taper, and that it can sometimes significantly improve the convergence of the method. For example, if a 64×64 grid size allows (with a taper) convergence in five iterations whereas a 42×42 grid size requires 23 iterations, a noticeable improvement in total computer time is effected. Also, there are cases where a taper must be introduced if the SIT method is to converge at all, without the application of a full orthogonalization procedure. The technique requires a correct choice of arbitrary values in the extended matrix, and guidelines are presented for such a choice     

并行FDTD方法在海面及其上方漂浮目标复合电磁散射中的应用

利用基于图形处理器(Graphics Processing Unit, GPU)的并行时域有限差分(Finite Difference Time Domain, FDTD)法计算一维粗糙海面及其上方二维漂浮目标的复合电磁散射.采用各向异性完全匹配层(Uniaxial Perfectly Matched Layer, UPML)吸收边界作为截断边界, 为了便于并行程序的设计, 在整个计算区域使用UPML吸收边界差分公式进行迭代.利用异步通信技术来隐藏主机和设备之间的通信时间, 同时使用片上的共享存储器提高读取速度, 进一步对程序进行优化, 得到很好的加速比, 证明了该方法的计算高效性.通过与串行FDTD法以及串行矩量法获得的数值结果进行比较, 验证了该并行方法的正确性, 进而研究了海面上方类似舰船漂浮目标的电磁散射特性, 讨论了入射角、海面风速以及目标吃水深度对双站散射系数的影响.     

Electromagnetic scattering from a wire grid parallel to a planar stratified medium

The theory for electromagnetic scattering from a special periodic structure adjacent to a stratified medium is given. The configuration consists of a parallel grid of thin wires that are located in a plane parallel to a planar stratified region. The case where the grid is outside the stratified half-space is considered first. Subject to the restriction on the thinness of the grid wires, an exact solution for the scattered fields is obtained. The final result, for the far-field scattering and transmission, can be interpreted clearly in terms of an equivalent transmission line circuit. In this case, the grid is represented as a shunt element. Finally, the theory is generalized to allow for the situation where the grid is within the stratified region.