Smooth local cosine based Galerkin method for scattering problems

The smooth local trigonometric (SLT) functions are employed as the basis and testing functions in the Galerkin based method of moments (MoM), and sparse impedance matrices are obtained. The basic idea of SLT is to use smooth cutoff functions to split the function and to fold overlapping parts back into the intervals so that the orthogonality of the system is preserved. Moreover, by choosing the correct trigonometric basis, rapid convergence in the case of smooth functions is ensured. The SLT system is particularly suitable to handle electrically large scatterers, where the integral kernel behaves in a highly oscillatory manner. Numerical examples demonstrate the scattering of electromagnetic waves from two-dimensional objects with smooth contours as well as with sharp edges. A comparison of the new approach versus the traditional MoM and wavelet methods is provided.     

一种基于不连续伽辽金方法求解多区域目标散射问题的优化预处理器

在电磁散射问题中,由均匀介质和金属组合而成的多区域结构目标在天线仿真、雷达成像等工程问题中有着广泛应用.针对多区域目标的散射问题,研究了不连续伽辽金（discontinuous Galerkin, GD）方法在多区域面积分（surface integral equation, SIE）矩量法中的使用,同时提出了一种优化的距离稀疏预处理（optimized distance sparse preconditioner, O-DSP）方法.该方法根据阻抗矩阵中不同积分算子随距离变化的特性来个性化选择预处理矩阵,进一步增加了预处理矩阵的稀疏性.数值计算表明,相比之前的距离稀疏预处理方法,优化的预处理矩阵非零元素仅为以前的一半,而且具有相同加速迭代效果.     

Modal expansions for resonance scattering phenomena

This paper very briefly reviews certain approaches commonly used to predict scattering in the region between those amenable to either high or low frequency approximations. As an alternative to extensions of such approximations into this so-called "resonance region," the suggestion is made that the concept of modal expansions of fields be investigated. The existence of such characteristic modes is reasoned heuristically and certain speculations are presented concerning their properties and their determination.     

Spherical-harmonic expansions in near-field aerial problems

The spherical-harmonic expansion may be applied to a certain class of near-field aerial problems. The conditions for validity of the expansion and the associated convergence problems are discussed.     

Rayleigh hypothesis in scattering problems

It is shown that the validity of the Rayleigh hypothesis is dependent on the distribution of singularities in the analytic continuation of the exterior scattered field; the hypothesis is fulfilled if, and only if, these are concentrated in a sufficiently small domain. Conclusions reached by Burrows in a recent letter are criticised.     

Matrix description of scattering problems

A scattering matrix is proposed that predicts the radiation patterns of antennas near to scattering objects. The method has been applied to the 2-dimensional problem of a line source adjacent to a square scatterer, and excellent agreement has been obtained with experimental results.     

Nonuniqueness in inverse source and scattering problems

The fields radiated by spherically symmetric time-harmonic sources are used to illustrate how little can be learned about a source from knowledge of the radiated field outside of the source volume. It is shown that even if it is known that the source is spherically symmetric, it is not possible to determine its radial structure. Moreover, even if the radial structure of the source is known apart from a constant amplitude and a finite radius, it is not possible to evaluate those two unknowns independently. These examples are applied to demonstrate explicitly that two methods that have been claimed to produce exact unique solutions to inverse-source and inverse-scattering problems do not yield the claimed results.     

Fourier transforms in propagation and scattering problems

Three-dimensional Fourier transforms are applied to electromagnetic wave propagation problems. After obtaining functions in transform space, inversion and contour integration yield a plane wave integral representation.     

Analysis of electromagnetic scattering from conducting bodies ofrevolution using orthogonal wavelet expansions

The wavelet expansion method has been extended to study the electromagnetic scattering from conducting bodies of revolution. The magnetic field integral equation (MFIE) is solved by this approach. By expanding the induced surface currents in terms of Fourier series of uncoupled azimuthal cylindrical modes, a simplified MFIE is attained for each unknown mode current that varies along the curved profile of the scatterer. By applying the boundary element method (BEM), the curved profile is mapped into the definition domain of the orthogonal wavelets on the interval. The unknown mode currents are then expressed using multiscale wavelet expansions. The simplified MFIE is converted into a sparse, multilevel matrix equation by the Galerkin method. Numerical examples are provided to illustrate the merits of this wavelet approach     

A hybrid-iterative method for scattering problems

A new technique, named a hybrid-iterative method (HIM), is presented to solve the magnetic field integral equation (MFIE) for the induced currents on an arbitrary, perfectly conducting scatter. The technique is an evolution from two previous techniques developed earlier. The first of the previous techniques used the moment method (MM) to compute correction currents to an optics-type current. The second of the previous techniques effected a significant improvement by eliminating the use of the moment method to obtain the correction currents, using iteration to obtain them. The technique described here incorporates the edge diffraction theory and the Fock theory into the Ansatz of the iterative scheme. This procedure speeds up the algorithm as well as extending the range of problems that can be solved by the iterative scheme. Furthermore, the present technique incorporates the correction currents into the total currents thereby simplifying the iterative scheme. For intermediate size and larger bodies, the central processing unit (CPU) time is significantly less than that of the moment method. Results are presented for a variety of curved and edged two-dimensional cylinders illuminated by a transverse electric plane wave.     

Spurious fields in time-domain computations of scattering problems

Two-dimensional (2-D) electromagnetic scattering problems with a time-periodic incident field are considered. The scatterer is a perfect conductor, and an artificial boundary condition is used. The large-time behavior of solutions, depending on (divergence-free) initial conditions, is characterized. It turns out that in addition to the expected time-periodic solution, the limiting solution may also contain a spurious stationary field. The source of the stationary field is explained and equations describing it are obtained. Several avoidance strategies are discussed and numerical comparisons of these techniques are given     

大尺度电磁散射与逆散射问题的深度学习方法

大尺度电磁散射与逆散射一直是科学研究和工程应用的热点和难点,亟待发展将电磁模型与数据挖掘有机融合的高性能求解方法,针对此,提出了一种针对大尺度电磁散射与逆散射问题的深度学习模型.该模型不仅继承了深度神经网络结构简单、运算速度快等优点,而且还能高精度地解决大尺度电磁散射与逆散射问题.实验结果表明:文中提出的深度学习方法可为解决现有大尺度电磁测算融合和电磁逆散射的计算成本昂贵的难题提供新思路、开辟新方向.     

Solution of diffraction problems by means of the modified Galerkin method

Using the problem of matching of planar waveguides as an example, an approach to solution of diffraction problems with the help of the modified Galerkin method is considered.     

MoM-FDTD hybrid technique for analysing scattering problems

The authors present a new hybrid technique for analysing complex electromagnetic problems, combining a progressive version of the MoM and the FDTD. The use of the equivalence principle allows the problem to be separated into two simpler problems, and a proper set of equivalent sources is defined to account for the coupling between actual sources and scatterers     

一种新的基于混合域的数字音频水印

在数字水印的基础上,提出了一种基于DCT和DWT混合域的音频水印的算法。首先对原始的音频信号进行离散小波变换,得到音频信号的精细分量和近似分量,然后对这两种系数进行离散余弦变换,最后将两种不同的水印嵌入到两种系数。提取水印信息时,不管音频信号的长度如何,均采用相同的方法进行变换。实验证明,此方法可以实现不丢失音频信号的频率信息,在考虑嵌入的两种不同水印的顺序的原则下,实现嵌入和提取信息的同步。     

An iterative method for solving scattering problems

An iterative method is developed for computing the current induced by plane wave excitation on conducting bodies of arbitrary shape. In this method, the scattering body is divided into lit- and shadow-side regions separated by the geometric optics boundary. The induced current at any point on the surface of the scatterer is expressed as the sum of an approximate optics current and a correction current. Both of these currents are computed by iteration for the lit and shadow regions separately. The general theory is presented and applied to the problems of scattering from a two-dimensional cylinder of circular and square cross sections. The results are compared with the method of moments and good agreement is obtained. This method does not give erroneous results at internal resonances of the scatterer, does not suffer from computer storage problems and can be extended to nonperfect conductors as well as to three-dimensional bodies.     

一种多导体散射问题的快速宽频带分析

分块阻抗矩阵迭代算法(Block-Iterative Algorithm)是一种非常直接而有效的求解多导体散射的加速求解算法.然而当单导体尺寸较大时,求解多导体散射的宽频带特性时仍然存在较费计算资源问题.基此,提出采用一种有效的Pade逼近型[Z]阻抗矩阵内插技术与分块阻抗矩阵迭代算法相结合的方法来快速分析多导体的宽频带电特性;计算结果与已有结果吻合较好,并且大大节省了计算资源,从而说明了该方法的快速性和精确性.     

Numerical second-kind-integral-equation solutions of electromagnetic scattering problems

A new, highly accurate numerical method based on second-kind integral equations has been developed to solve electromagnetic scattering problems for closed conducting bodies in two dimensions. The method is approximately fourth-order convergent, owing to the use of accurate new quadrature formulas.<>     

Improved finite-difference formulation in frequency domain forthree-dimensional scattering problems

The finite-difference method in the frequency domain is a powerful tool for analyzing arbitrarily shaped transmission-line discontinuities and junctions. An improved formulation based on Maxwell's equations in integral form is presented. It corresponds to the Helmholtz equation and reduces the numerical efforts in solving the large linear equation system considerably. The method is verified by comparison to previous work on microstrip     

Concentration maximization and local basis expansions (LBEX) for linear inverse problems

Linear inverse problems arise in biomedicine electroencephalography and magnetoencephalography (EEG and MEG) and geophysics. The kernels relating sensors to the unknown sources are Green's functions of some partial differential equation. This knowledge is obscured when treating the discretized kernels simply as matrices. Consequently, physical understanding of the fundamental resolution limits has been lacking. We relate the inverse problem to spatial Fourier analysis, and the resolution limits to uncertainty principles, providing conceptual links to underlying physics. Motivated by the spectral concentration problem and multitaper spectral analysis, our approach constructs local basis sets using maximally concentrated linear combinations of the measurement kernels.