Edge-based FEM solution of scattering from inhomogeneous andanisotropic objects

This paper presents an application of the edge-based vector finite element method to scattering problems of anisotropic and inhomogeneous objects. Based on conventional FEM functional, a hybrid finite element-surface integral formulation is established by introducing permittivity and permeability tensors. The space domain is divided into interior and exterior regions by an imaginary surface conformal to the scatterer. Edge vector finite elements are used to model the anisotropic and inhomogeneous interior, and a surface integral equation is used to model the unbounded exterior. Compared to other hybrid techniques, the approach here retains the symmetry and sparsity of the FEM matrix and introduces only one type of unknown equivalent current in the moment matrix equation. To validate the theory, typical 2-D numerical results are first presented, which show excellent agreement with exact eigenmode expansion solutions or accurate MoM data     

On the scattering of arbitrary shape microstrip patch

In this letter, discrete complex image method is employed to compute the Green‘s functions in the spatial domain, which improves the speed of evaluating the impedance matrix. The triangle vector basis function--RWG, is used to simulate the current distribution in order to compute the scattering properties of arbitrary shape microstrip patch without the staircase approximation. The numerical result shows the validity of the proposed method.     

A weak form of the conjugate gradient FFT method for plate problems

A number of electromagnetic field problems for planar structures can be formulated in terms of a hypersingular integral equation, in which a grad-div operator acts on a vector potential. The vector potential is a convolution of the free-space Green's function and some surface current density over the domain of interest. A weak form of this integral equation is obtained by testing it with subdomain basis functions defined over the plate domain only. As a next step, the vector potential is expanded in a sequence of subdomain basis functions and the grad-div operator is integrated analytically over the plate domain only. For the problem of electromagnetic scattering by a plate, the method shows excellent numerical performance. The numerical difficulties encountered in some previous conjugate gradient fast Fourier transform (CGFFT) methods have been eliminated     

A general expression of dyadic Green's functions in radiallymultilayered chiral media

A general expression of spectral-domain dyadic Green's function (DGF) is presented for defining the electromagnetic radiation fields in spherically arbitrary multilayered and chiral media. Without any loss of the generality, each of the radial multilayers could be the chiral layer with different permittivity, permeability, and chirality admittance, while both distribution and location of current sources are assumed to be arbitrary. The DGF is composed of the unbounded DGF and the scattering DGF, based on the method of scattering superposition. The scattering DGF in each layer is constructed in terms of the modified and normalized spherical vector wave functions. The coefficients of the scattering DGFs are derived and expressed in terms of the equivalent reflection and transmission coefficients, by applying boundary conditions satisfied by the coefficient matrices     

目标电磁散射极点的不变性特征分析

对频域磁场积分方程在离散化的基础上进行了矢量分析，发现离散化后的矩阵方程中含有频率因子的算子矩阵仅包含了反映散射体形状的矢量信息，从而得出极点的分布只依赖于目标的外部形状信息这一结论；然后利用FDTD进行了仿真研究，从不同姿态角(散射方向)的后时响应数据中提取了极点，结果保持了较好的一致，进一步证实了目标姿态角的改变不会影响极点的分布这一特征。     

Postprocessing of 3-D current density reconstruction results with equivalent ellipsoids

A method of postprocessing and visualizing three-dimensional vector fields, such as current density reconstruction results, is presented. This method is based on equivalent ellipsoids fitted to the vector fields. The technique has been tested with simulated data and current density reconstructions based on bioelectromagnetic data obtained from a physical thorax phantom. Three different approaches based on: 1) longest distance; 2) dominant direction; and 3) principal component analysis, for fitting the equivalent ellipsoids are proposed. Multiple foci in vector fields are extracted by multiple ellipsoids which are fitted iteratively. The method enables statistical postprocessing for the sake of comparisons of different source reconstructions algorithms or comparisons of groups of patients or volunteers.     

Analysis of two dimensions sparse multicylinder scattering problem using DD-FDTD method

An algorithm of two-dimensional (2-D) domain decomposition finite-difference time-domain (DD-FDTD) using in sparse multicylinders scattering problem is proposed in this paper. The idea of domain decomposition is introduced to divide the sparse problem domain into several subdomains. All of subdomains are connected by means of the 2-D time domain Green's function. As a result, a great deal of meshes memory between cylinders is removed, especially when the distances between cylinders become large. Furthermore, the coupling between cylinders can be regarded as the equivalent cylindrical wave irradiations. The incident signals of the equivalent cylindrical waves are expressed as cylindrical wave input field array (CWIFA) according to Huygens principle. Then the calculation time is significantly reduced. The near-field to far-field transformation is used to obtain the equivalent cylindrical wave; as a result, the calculation time can be reduced further. The new method has been demonstrated in 2-D multicylinders scattering problem. Numerical results are in good agreement with the results obtained using classical FDTD method and moment of methods (MM).     

A recursive single-source surface integral equation analysis for wave scattering by heterogeneous dielectric bodies

The problem of electromagnetic wave scattering by heterogeneous dielectric bodies is formulated in a recursive manner by organizing their homogeneous subregions into hierarchical multiply-nested structures. The inner details of each multiply-nested body are completely accounted for by an equivalent surface representation that yields the electric and magnetic fields tangent to the body only in terms of a single unknown electric surface current density distributed on its outer surface. In this manner, the problem of wave scattering by heterogeneous dielectric bodies is reduced to a scattering problem over their outermost surfaces in terms of only a single unknown current density. For a large number N of different homogeneous dielectric subregions within such a heterogeneous body, the proposed method has a computational complexity of O(N/sup 1.5/) and storage requirements that increase in proportion to O(N). Furthermore, the equivalent surface representation derived for a particular subregion is invariant under rotation and translation and may, therefore, be applied to identical subregions without repeating the computation. The fields at any interior points are calculated by a fast backward recursion.     

钝角二面角全极化双基地RCS统计建模

钝角二面角结构在目标的隐身特性中发挥着重要作用,但其双基地特性尚不明确.采用电磁仿真与统计建模相结合的方法,从频域、空域、极化域和统计分布角度对其双基地散射特性进行分析.研究表明,在电尺寸较小时,双基地散射增强特性并不明显,单/双基地RCS概率密度分布差异大,共极化的双基地RCS概率密度分布呈现双峰特性,为此提出了双对...     

Computation of mutual coupling between slot-coupled microstrippatches in a finite array

An analytical method is presented for the evaluation of mutual coupling between slot-coupled microstrip patches in a finite array. The approach is a combination of the equivalence principle and the reciprocity theorem and uses the spectral domain Green's functions for a dielectric slab in a moment method solution for the unknown patch and slot current distribution. The excitation mechanism of the patches is taken into account by introducing an N-port equivalent network, and the impedance matrix of an array of N-element slot-coupled patches is evaluated directly from its network voltage and current matrices of order N². As examples, the mutual impedances and scattering coefficients for two-, four-, and eight-element arrays are evaluated. Results are compared with measured data     

A weak form of the conjugate gradient FFT method fortwo-dimensional TE scattering problems

The problem of two-dimensional scattering of a transversal electric polarized wave, by a dielectric object is formulated in terms of a hypersingular integral equation, in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free-space Green's function and the contrast source over the domain of interest. A weak form of the integral equation for the unknown electric flux density is obtained by testing it with rooftop functions. The vector potential is expanded in a sequence of the rooftop functions and the grad-div operator is integrated analytically over the dielectric object domain only. The method shows excellent numerical performance     

Numerical Simulation Bistatic Scattering from Three-Dimensional Conducting Rough Surface with UV Multilevel Partitioning Method Using Pulse Vector Basic Function

Vector wave three-dimensional (3D) conducting rough surface scattering problem solved by a UV method with multilevel partitioning procession (UV-MLP) using pulse vector basic function is developed in this paper, in which pulse vector basic function is more appropriately to be used for truly describe the vector inducted currents’ distribution along 3D PEC rough surface. For a 3D conducting rough surface scattering problem, the scattering structure is partitioned into multilevel blocks. By investigating the rank in the static problem, the impedance matrix for given transmitting and receiving blocks is expressed into products of U and V matrices. The UV method is illustrated by applying to a 3D scattering problem of random conducting rough surface. Finally, numerical simulation results are carried and discussed.     

Reflection from a periodically perforated plane using a subsectional current approximation

The scattering from a zero thickness plane having finite sheet resistance and perforated periodically with apertures is calculated for arbitrary plane wave illumination. The surface current density within the unit cell is approximated by a finite number of current elements having rooftop spatial dependence. The transverse electric field is expressed in terms of the current, and the electric field boundary condition is satisfied in an integral sense over the conductor, generating a finite dimension matrix equation whose solution is the current density. Since the conductor shape is defined through the locations of subsectional current elements, arbitrary shaped apertures can be handled. The reflection coefficient and current distribution are calculated for square apertures in both perfectly conducting and resistive sheets, and for cross-shaped apertures. Finite resistivity is shown to cause the magnitude of the transverse magnetic (TM) reflection coefficient to decrease more rapidly and its phase to decrease less rapidly, as the angle of incidence approaches glancing. Through detailed plots of the current density, the current crowding around the apertures is made clearly evident.     

缝隙阵列的时域溅射特性研究

时域溅射,是散射体结构不同部分产生的散射回波在远场叠加时,其时域波形在开始部分出现的不稳定的现象.对于低散射目标,只有在回波叠加稳定后,其散射电场的幅度才变得很低,而在开始的几个电波周期内会有比较强的散射电场.本文对缝隙阵列的时域溅射特性进行研究,采用周期边界时域有限差分（Finite-Difference Time-Domain,FDTD）算法对不同尺寸的缝隙阵列的时域溅射特性进行了仿真,提取了其等效电路参数,并采用等效电路法分析了缝隙宽度引起的并联电容对正弦波时域溅射和高斯脉冲时域散射特性的影响.分析结果发现：当并联电容降低的时候,时域反射系数的包络值下降速度增加,导致溅射现象的最大值降低.理论结果得到了实验验证.     

The three dimensional weak form of the conjugate gradient FFTmethod for solving scattering problems

The problem of electromagnetic scattering by a three-dimensional dielectric object can be formulated in terms of a hypersingular integral equation, in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free space Green's function and the contrast source over the domain of interest. A weak form of the integral equation for the relevant unknown quantity is obtained by testing it with appropriate testing functions. The vector potential is then expanded in a sequence of the appropriate expansion functions and the grad-div operator is integrated analytically over the scattering object domain only. A weak form of the singular Green's function has been used by introducing its spherical mean. As a result, the spatial convolution can be carried out numerically using a trapezoidal integration rule. This method shows excellent numerical performance     

Application of maximum likelihood estimation to radar imaging

An efficient maximum likelihood (ML) estimator to obtain the scattering center locations of a target and the relative scattering level of these scattering centers from the scattered field data is described. In the proposed method, ML estimation is carried out in the image domain rather than in the frequency-aspect domain. A two-dimensional (2-D) inverse Fourier transform is used to transfer the scattered field data from frequency-aspect domain to the image domain (down-range/cross-range). As expected, the scattered field data in the image domain has some regions with high energy. The samples in the high-energy regions are used to obtain the initial guess for the ML estimator as well as for ML estimation. The ML estimator in the image domain is applied to both simulated and experimental scattered fields of some targets     

A spectral domain method for multiple scattering in discrete randommedia

In an earlier paper (see ibid., vol.36, p.1114-28, 1988) a spectral-domain method was developed for analyzing multiply scattered scalar wavefields propagating in continuous random media. This method is extended to accommodate vector wavefields propagating in discrete random media. The two-dimensional Fourier spectra of vector wavefields propagating in the forward and backward directions are characterized by a pair of coupled first-order differential equations. Dyadic scattering functions characterize the local interaction of the wavefields with the random medium. The results are restricted to sparse distributions whereby the dyadic scattering functions are easily computed. The first- and second-order moments of the vector wavefields can be computed by invoking an assumption essentially equivalent to the Markov approximation as it is applied to scalar wavefields propagating in continuous random media. A complete solution for the coherent wavefield is derived and compared to known results. The results are essentially equivalent to those obtained by using the effective field approximation     

Dielectric medium

The concept of the generalized scattering amplitude is applied to the electromagnetic (EM) scattering of an arbitrarily shaped, perfectly conducting object partially immersed in a semi-infinite dielectric medium. The dielectric medium can have either electric loss or magnetic loss or both. In a two-dimensional (2-D) formulation, after the outgoing cylindrical wave is factored out from the scattered wave, the remaining wave envelope component in the scattered wave is defined as the generalized scattering amplitude. The transformed Helmholtz equation in terms of the generalized scattering amplitude can be solved numerically using a finite-difference method over the entire scattering domain including both the semi-infinite free-space (vacuum or air) and the semi-infinite dielectric medium. Example problems of scattering by infinitely long, perfectly conducting cylinders of circular and trapezoidal ship-shaped cross sections are solved to demonstrate the theoretical formulation and numerical method. The radial profiles of the generalized scattering amplitude and the total field over the entire scattering region are also presented, and their properties are discussed. The far-field bistatic cross section and induced current density on the obstacle's surface are also presented. These results show that the method can be used to yield complete and accurate solutions to 2-D EM scattering problems involving arbitrarily shaped metallic objects partially immersed in a penetrable semi-infinite dielectric medium     

Numerical study on an equivalent source model for inhomogeneous magnetic field dosimetry in the low-frequency range

A new equivalent numerical source model is proposed for efficient dosimetric investigations in the low-frequency range. This approach allows the reproduction of complicated inhomogeneous magnetic field distributions around electronic appliances with full generality (i.e., supports three-dimensional vector fields). This paper investigates the accuracy of the equivalent source model using the geometry-based numerical reference model of a current loop to simulate the magnetic field distribution of a real electronic appliance. Good agreement between the equivalent source model and the reference is obtained with regard to the magnetic field distribution and the induced electric current density in a homogeneous human body model, respectively.     

A new approach based on a combination of integral equation and asymptotic techniques for solving electromagnetic scattering problems

We introduce a new approach for combining the integral equation and high frequency asymptotic techniques, e.g., the geometrical theory of diffraction. The method takes advantage of the fact that the Fourier transform of the unknown surface current distribution is proportional to the scattered far-field. A number of asymptotic methods are currently available that provide good approximation to this farfield in a convenient analytic form which is useful for deriving an initial estimate of the Fourier transform of the current distribution. An iterative scheme is developed for systematically improving the initial form of the high frequency asymptotic solution by manipulating the integral equation in the Fourier transform domain. A salient feature of the method is that it provides a convenient validity check of the solution for the surface current distribution by verifying that the scattered field it radiates indeed satisfies the boundary conditions at the surface of the scatterer. Another important feature of the method is that it yields both the induced surface current density and the far-field. Diffraction by a strip (two-dimensional problem) and diffraction by a thin plate (three-dimensional problem) are presented as illustrative examples that demonstrate the usefulness of the approach for handling a variety of electromagnetic scattering problems in the resonance region and above.