任意形状导体介质混合目标的瞬态电磁散射特性分析

通过建立自由空间内多个导体介质混合目标的理论模型,根据电磁场等效原理和边界条件,建立了求解任意形状导体介质混合目标散射特性的时域电场积分方程(TDEFIE).导出了TDEFIE的时间步进算法(MOT)矩阵方程,并应用基于隐式MOT算法的TDEFIE对任意形状导体介质混合目标进行了瞬态分析,其数值结果说明了该算法的有效性.     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

Numerical solution of integral equations for dielectric objects ofprismatic shapes

A numerical method to investigate scattering from dielectric geometries of prismatic shapes has been developed. The surface integral equations are formulated by Schelkunoff's equivalence principle in terms of equivalent surface electric and magnetic currents. To solve these integral equations for the unknown currents, the object's cross-section is mapped onto a circle. In the transformed space, Fourier type entire-domain basis functions are used in the cross section and triangular subdomain basis functions are selected along the generating curve to represent the currents. A moment method is then used to reduce the integral equations to a matrix equation to compute the current coefficients. It is found that the transformation of the object's surface to a circular shape improves the convergence of the current mode in the cross-section. However, the current modes are coupled on the surface and the matrix equation includes all the modes     

A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies

A method for calculating the electromagnetic scattering from and internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies is presented. A volume integral equation is formulated and solved by using the method of moments. Tetrahedral volume elements are used to model a scattering body in which the electrical parameters are assumed constant in each tetrahedron. Special basis functions are defined within the tetrahedral volume elements to insure that the normal electric field satisfies the correct jump condition at interfaces between different dielectric media. An approximate Galerkin testing procedure is used, with special care taken to correctly treat the derivatives in the scalar potential term. Calculated internal field distributions and scattering cross sections of dielectric spheres and rods are compared to and found in agreement with other calculations. The accuracy of the fields calculated by using the tetrahedral cell method is found to be comparable to that of cubical cell methods presently used for modeling arbitrarily shaped bodies, while the modeling flexibility is considerably greater.     

Analysis of arbitrarily shaped dielectric radomes using adaptive integral method based on volume integral equation

The adaptive integral method (AIM) is employed to solve the volume integral equation (VIE) for analyzing the radiation of the antenna with an arbitrarily shaped radome. Small dipoles are used as exciting sources. Modeling the radomes by tetrahedron cells, the induced volume current is determined by the AIM based on VIE. The application of AIM significantly reduces CPU time and computer memory requirement. Hence, the method presented in the paper can be applied to simulate electrically large sized radomes. Finally, the radiation patterns of small dipole arrays in the presence of spherical and conical radomes are calculated.     

Numerical analysis of arbitrarily shaped discontinuities betweenplanar dielectric waveguides with different thicknesses

An approach that combines the finite-element and boundary-element methods is applied to the analysis of arbitrarily shaped discontinuities between planar dielectric waveguides with different thicknesses. The fields interior and exterior to the region enclosing the discontinuities are treated by the finite-element method and the boundary-element method, respectively. The waveguide regions connected to the discontinuities are handled by analytical solutions. In this approach, scattering characteristics of the discontinuities can be accurately evaluated, and far-field radiation patterns can be easily calculated. To show the validity and usefulness of this approach, the scattering characteristics of a step, a staircase transformer, and a tapered transformer are analyzed. Also, a simple equivalent network approach is introduced for estimating the reflection and transmission characteristics of planar dielectric waveguide discontinuities, and the effectiveness of this simple approach is confirmed by comparing the numerical results with those of the approach that combines the finite-element and boundary-element methods     

任意形状天线罩的快速分析

将自适应积分算法与体积分方程相结合分析任意形状天线罩对天线辐射特性的影响。将任意形状的天线罩剖分成四面体，基于体积分方程的自适应积分快速算法求出天线罩上的感应电流，即可求出天线-天线罩系统的总场。自适应积分快速算法的应用提高了矩量法的计算速度，并大大缩减了需要的存储量，从而使该方法可用于分析电尺寸较大的天线罩.最后,分别计算了球形、锥形天线罩存在时理想电振子阵列的辐射方向图。     

Electromagnetic scattering from 3-D curved dielectric bodies usingtime-domain integral equations

A boundary integral equation (BIE) approach is developed to calculate transient scattering from dielectric bodies. The treatment is directly in terms of the E and H fields rather than magnetic and electric currents. It employs curvilinear (quadratic) modeling, which allows accurate representation of arbitrarily shaped curved bodies. The treatment is isoparametric with the same quadratic representation of the spatial field variation and with the temporal variation modeled by similar quadratic elements. Integration employs high-order Gaussian quadrature with special treatment of the singular and hypersingular integrals that arise. The treatment is implicit, requiring the solution of a sparse matrix equation at each timestep. This adds only trivially to the cost at each timestep and, by freeing the timestep from the constraint that it be smaller than the smallest nodal spacing, can greatly reduce the number of timesteps that must be employed. Additionally, it produces stable results without resort to the averaging processes proposed elsewhere. Example calculations of scattering from a sphere, a cube, and an almond are presented and compared with earlier published transient results and with results from a frequency domain treatment. Good agreement and improved accuracy is found     

Radar cross section of arbitrarily shaped bodies of revolution

The radar cross section (RCS) of an arbitrarily shaped, homogeneous dielectric body of revolution (BOR) is evaluated by the surface integral equation (SIE) formulation and the method of moments. Method accuracy is verified by the good agreement with the exact solutions for the RCS of a dielectric sphere. To demonstrate the advantages of this method, the RCS for a complex BOR model of human torso is computed with a nonaxially incident plane wave. Seven Fourier modes are considered in the computation. The SIE and approximate integral equation (AIE) formulations are next given for the RCS evaluation of a composite dielectric and conducting BOR. For the cases considered, both formulations give the same surface currents and RCS results. However, significant savings in computer storage and CPU time are realized for the AIE approach, since only one current (electric or magnetic) need be determined for RCS evaluation     

Computer-aided analysis of a finite arbitrarily shaped dielectric antenna

A numerical method of analysis is developed to determine the characteristics of a homogeneous dielectric antenna of arbitrary shape based on a general expression of electromagnetic wave scattering by a homogeneous dielectric body derived by Barrar and Dolph. This method is tested on a dielectric-disk antenna.     

Extended boundary condition integral equations for perfectly conducting and dielectric bodies: Formulation and uniqueness

The equivalence theorem is used to derive novel generalized boundary condition (GBC) integral equations for the tangential components of the electric and magnetic fields on the interfaces of a finite number of dielectric or conducting scatterers. Closed surface, plane, and line extended boundary conditions (EBC) equivalent to the GBC are introduced. The GBC integral equations can now be replaced by any of these EBC integral equations whose solutions are unique and easy to obtain numerically using the moment method. A perfectly conducting sphere and a dielectric sphere in the electrostatic field of two equal and opposite point charges are presented as simple examples of the general procedure.     

Numerical analysis of arbitrarily shaped probe-excited single-armprinted wire antennas

A general integral equation technique is described for analysis of an arbitrarily shaped single-arm printed wire antenna excited through a vertical probe. A unified current integral equation is formulated on the basis of dyadic Green's functions and the reciprocity theorem. The current distribution is obtained by using a parametric moment method in which parameter segments are adopted for the printed wire instead of the commonly employed wire length segments. The radiation field solution involving both the printed antenna and vertical probe is also presented. The validity of the formulation is verified by comparing the numerically obtained input impedance and radiation patterns for a linear antenna and a meander antenna with measured data. A circular open loop and an Archimedian spiral are investigated to illustrate the applicability of the present technique     

Time domain adaptive integral method for surface integral equations

An efficient marching-on-in-time (MOT) scheme is presented for solving electric, magnetic, and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium. The proposed scheme is the extension of the frequency-domain adaptive integral/pre-corrected fast-Fourier transform (FFT) method to the time domain. Fields on the scatterer that are produced by space-time sources residing on its surface are computed: 1) by locally projecting, for each time step, all sources onto a uniform auxiliary grid that encases the scatterer; 2) by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global, multilevel/blocked, space-time FFTs; 3) by locally interpolating these fields back onto the scatterer surface. As this procedure is inaccurate when source and observer points reside close to each other; and 4) near fields are computed classically, albeit (pre-)corrected, for errors introduced through the use of global FFTs. The proposed scheme has a computational complexity and memory requirement of O(N/sub t/N/sub s/log/sup 2/N/sub s/) and O(N/sub s//sup 3/2/) when applied to quasiplanar structures, and of O(N/sub t/N/sub s//sup 3/2/log/sup 2/N/sub s/) and O(N/sub s//sup 2/) when used to analyze scattering from general surfaces. Here, N/sub s/ and N/sub t/ denote the number of spatial and temporal degrees of freedom of the surface current density. These computational cost and memory requirements are contrasted to those of classical MOT solvers, which scale as O(N/sub t/N/sub s//sup 2/) and O(N/sub s//sup 2/), respectively. A parallel implementation of the scheme on a distributed-memory computer cluster that uses the message-passing interface is described. Simulation results demonstrate the accuracy, efficiency, and the parallel performance of the implementation.     

Volume integral equations for analysis of dielectric branchingwaveguides

Novel forms of volume integral equations are developed for the exact treatment of wave propagation in two-dimensional dielectric branching waveguides. The integral equations can be obtained by considering the condition at a point far away from the junction section. An approximate solution by the Born approximation and a numerical solution by the moment method establish the validity of the new volume integral equations. The numerical results are discussed from the viewpoint of energy conservation and reciprocity. The solution is exact if sufficiently large computer memory and computational time are used. The method can be extended to problems of a more general nature (i.e. the incident TM mode), and complex configurations of branching waveguides. The basic idea is also applicable to techniques using boundary (surface) integral equations which are applicable to three-dimensional problems     

A full-wave analysis of an arbitrarily shaped dielectric waveguideusing Green's scalar identity

An integral equation analysis is proposed to determine the phase constant of an arbitrarily shaped dielectric waveguide. The main feature of this approach is the use of Green's scalar identity in which only simple contour integrals have to be evaluated. Different scalar Green's functions are considered to satisfy the boundary conditions for the electric and magnetic fields in each region. This approach is combined with the boundary element technique with linear elements for the computation. The case of the rectangular dielectric image waveguide is discussed. and numerical results are shown to be consistent with other theories and experiments. The cases of hollow rectangular and semicircular image waveguides are analyzed, and numerical results are presented     

透层天线电流积分方程的数值解

在已有的三层有耗媒质中的透层天线（ＢＰＡ）电流积分方程的基础上,给出了电流积分方程中的索末菲积分的低频近似解析公式并给出了其物理解释。利用三项式全域电流基函数,求得了透层天线的输入阻抗。采用静态场近似方法,很方便的求出了透层天线在地面的电场分布。     

The analysis of arbitrarily shaped aperture-coupled patch antennasvia a mixed-potential integral equation

A mixed-potential integral equation (MPIE) is formulated for the electric and magnetic currents on a multilayered aperture-coupled patch antenna. The integral equation is solved via the method of moments (MoM) using subsectional basis functions that allow the analysis of nonrectangular aperture and patch shapes. The input impedance and radiation efficiency of various aperture-coupled elements are calculated using the proposed technique and compared to measured results. The advantages and disadvantages of several aperture and patch configurations are discussed, and six methods of numerically de-embedding the element's input impedance are compared     

Iterative integral equation solution for cylindrical dielectric resonator

An exact integral equation describing the substrate-mounted open cylindrical dielectric resonator is derived, and a first approximate solution for the fundamental resonant mode is calculated. Results are presented and are compared with both experiment and another theoretical approach.     

A comparison of integral equations with unique solution in theresonance region for scattering by conducting bodies

A comparison of integral equations, for problems involving scattering by arbitrary-shape conducting bodies, having a unique solution in the resonance region is presented. The augmented electric and magnetic field integral equations and the combined field integral equation, in their exact and approximate versions, are considered. The integral equations and the basis and test functions used in the method of moments to solve them are reviewed. Their implementation in a computer code is analyzed, mainly the relation between the matrix properties and the CPU time and memory. Numerical results (condition number and backscattering cross section) are presented for the cube. It is shown that the combined field integral equation, and the approximate (symmetric) combined field integral equation, are the most efficient equations to use in the neighborhood of resonant frequencies, because the overdetermined augmented integral equations require an extra matrix multiplication     

An integral equation for electromagnetic scattering from homogeneous dielectric bodies

A single surface integral equation for problems involving electromagnetic scattering from homogeneous dielectric bodies illuminated by time-harmonic sources is developed via the equivalence principle. The equation is formulated in terms of an equivalent electric current defined at the body surface. When allowed to radiate in a homogeneous medium having the material parameters of the exterior medium of the original problem, the electric current solution to the integral equation produces the correct scattered electric and magnetic fields external to the body.