金属介质混合目标电磁特性的快速分析

将自适应积分算法与基于体面混合积分方程的矩量法相结合快速分析任意结构金属/介质混合目标的电磁散射和辐射特性.通过将传统矩量法的阻抗矩阵分为两部分且采用不同的方法进行处理计算,提高了矩量法的计算速度并大幅度缩减了需要的计算机内存占用量.最后,分别用传统的矩量法与结合自适应积分快速算法的矩量法计算了三个典型例子,通过比较充分说明了文中方法的有效性.     

金属-各向异性介质体组合目标频域体表积分方程矩量法

利用体表积分方程矩量法求解了具有任意的介电常数张量和磁导率张量的各向异性介质与金属的组合目标的电磁散射问题.给出了基于RWG面基函数和SWG体基函数的体表积分方程阻抗矩阵元素表达式并详细推导了阻抗矩阵元素所涉及的各种积分运算的计算方法;通过数值计算实例与解析解或其它数值方法的详细对比分析,证明了计算公式的正确性.     

Higher order hierarchical discretization scheme for surface integral equations for layered media

This paper presents an efficient technique for the analysis of electromagnetic scattering by arbitrarily shaped perfectly conducting objects in layered media. The technique is based on a higher order method of moments (MoM) solution of the electric field, magnetic field, or combined-field integral equation. This higher order MoM solution comprises higher order curved patches for the geometry modeling and higher order hierarchical basis functions for expansion of the electric surface current density. Due to the hierarchical property of the basis functions, the order of the expansion can be selected separately on each patch depending on the wavelength in the layer in which the patch is located and the size of the patch. In this way, a significant reduction of the number of unknowns is achieved and the same surface mesh can be reused in a wide frequency band. It is shown that even for fairly large problems, the higher order hierarchical MoM requires less memory than existing fast multipole method (FMM) or multilevel FMM implementations.     

Analysis of transient scattering from composite arbitrarily shapedcomplex structures

A time-domain surface integral equation approach based on the electric field formulation is utilized to calculate the transient scattering from both conducting and dielectric bodies consisting of arbitrarily shaped complex structures. The solution method is based on the method of moments (MoM) and involves the modeling of an arbitrarily shaped structure in conjunction with the triangular patch basis functions. An implicit method is described to solve the coupled integral equations derived utilizing the equivalence principle directly in the time domain. The usual late-time instabilities associated with the time-domain integral equations are avoided by using an implicit scheme. Detailed mathematical steps are included along with representative numerical results     

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.     

各向异性材料涂覆目标电磁散射特性仿真

该文基于阻抗边界条件(IBC),提出了3维各向异性材料涂覆目标电磁散射特性的矩量法(MoM)解决方案。根据表面等效原理,采用感应电磁流以3维RWG(Rao-Wilton-Glisson)矢量基函数展开的伽略金法。以表面阻抗矩阵表征电磁参数,实现各向异性材料涂覆目标的电磁仿真,算例结果与Mie级数解等精确结果吻合良好。对各向异性材料涂覆复杂目标的电磁散射特性进行分析,为目标的雷达隐身和反隐身提供理论支持。     

An Efficient Volume Integral Equation Solution to EM Scattering by Complex Bodies With Inhomogeneous Bi-Isotropy

A generalized volume integral equation method is formulated for electromagnetic scattering by arbitrarily shaped complex bodies with inhomogeneous bi-isotropy. Based on the volume equivalence principle, the integral equations are represented in terms of a pair of coupled bi-isotropic polarized volume electric and magnetic flux densities. Reduction of the integral equations into the corresponding matrix equations is obtained using the method of moments (MoM) combined with the tetrahedral mesh. In the MoM solution, the three-dimensional solenoidal function is incorporated as the basis function defined over each tetrahedral element and the details of implementation, particularly the treatment of integral singularities, will be elucidated. The efficiency and accuracy of the proposed method are validated by illustratively supported examples.     

Solution of combined-field integral equation using multilevel fastmultipole algorithm for scattering by homogeneous bodies

We present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of the CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ the MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects     

利用UTD修正的MoM-PO混合算法研究

介绍了利用矩量法(MoM)和物理光学(PO)混合方法处理复杂线体结构的电磁散射问题，提出利用pulse基函数对线电流进行展开，使得处理复杂线体结构问题变得简化，并推导出一般的矩阵方程。然后针对PO在阴影区域失效等问题，利用UTD(一致性几何绕射)对该简化模型结构下的PO区域电流进行了修正，使得其应用范围得到扩展、计算精度得到提高。文中的实例结果与传统的MoM很好的一致，从而说明了该方法的有效性和精确性。     

任意截面非均匀各向异性阻抗柱体的电磁散射

采用矩量法(MoM)结合阻抗边界条件研究了二维无限长任意形状截面非均匀各向异性阻抗柱体的电磁散射特性。散射场通过Stratton-Chu电场积分方程、电流连续性方程和二维格林函数予以求解。当柱体截面矢径的模等于恒定值时,目标退化为二维无限长圆柱,提出的计算方法仍然有效。计算得到的散射宽度结果与解析法、物理光学法(PO)的结果进行了比较,吻合良好。     

任意形状导体目标的极点求解

从理论上求解极点,频域矩量法结合围线积分是通用且准确的方法,但由于计算量大而一直用于处理旋转对称目标的求解.本文提出Chebyshev多项式展开格林函数的方法,把频率因子从电场积分方程中分离出来,实现了多频点矩量法的快速计算,解决了任意形状导体目标极点的求解问题.最后对围线积分方法进行适当改进,并求解了三种目标的极点.     

Scattering by Conducting Bodies Coated With Bi-Isotropic Materials

Electromagnetic scattering by arbitrarily shaped conducting bodies coated with general bi-isotropic materials is formulated in terms of the surface integral equation method. In order to facilitate the implementation of the surface equivalence principle, a field decomposition scheme is utilized to split a bi-isotropic media into two equivalent isotropic media. By enforcing the boundary condition on the interfaces of the body, a set of coupled integral equations is finally obtained for the unknown surface currents and then numerically solved using the moment methods combined with the vector triangular basis function. The fast multipole technique has been embedded into the algorithm to accelerate the solution process. The validity of theoretical formulations is verified by numerical results and their comparisons. The calculated results for bi-isotropically coated conducting spheres and oblate spheroids are compared with the exact solution and the existing data, and excellent agreements are observed.     

A volume-surface integral equation method for solving Maxwell'sequations in electrically inhomogeneous media using tetrahedral grids

Starting with the solution of Maxwell's equations based on the volume integral equation (VIE) method, the transition to a volume-surface integral equation (VSIE) formulation is described. For the VSIE method, a generalized calculation method is developed to help us directly determine E fields at any interface combination in three-dimensional (3-D) electrically inhomogeneous media. The VSIE implementation described is based on separating the domain of interest into discrete parts using nonuniform tetrahedral grids. Interfaces are described using curved or plane triangles. Applying linear nodal elements, a general 3-D formulation is developed for handling scatter field contributions in the immediate vicinity of grid nodes, and this formulation is applicable to all multiregion junctions. The special case of a smooth interface around a grid node is given naturally by this formulation. Grid nodes are split into pairs of points for E-field calculation, and node normals are assigned to these points. The pairs of points are assigned to the elements adjoining the grid node. For each pair of points, the correct field jumps on the interface are given by a surface integral over the polarization surface charge density     

混合ACA和MLFMA方法计算复合目标电磁散射

采用矩量法(MoM)计算电大尺寸的复合目标的电磁散射。为了能够高效快速地计算电大尺寸三维复合目标的电磁散射,提出一种新的混合方法,将自适应交叉近似(ACA)算法和多层快速多级子(MLFMA)算法相结合,共同加速矩量法的计算。其中,MLFMA用于加速目标与自身的作用,ACA用于加速目标与其他目标的相互作用。提出的混合算法在计算复合目标电磁散射时,可降低运算存储,缩短阻抗矩阵填充时间,并且能够加快矩阵矢量乘,且不影响计算精确度。数值算例表明,所提快速算法能够在保证电磁散射计算精确度前提下,比传统方法更高效。     

Moment method with isoparametric elements for three-dimensionalanisotropic scatterers

A new method for computing the frequency-domain electromagnetic fields scattered from, and penetrating into, arbitrarily shaped, three-dimensional, lossy, inhomogeneous anisotropic scatterers is presented. The method is based on a general volume integro-differential formulation of the scattering problem, and consists of the numerical solution of the coupled integral equations by the moment method and point matching. A particularly powerful feature of this method is that the numerical model of the scatterer is obtained by parametric volume elements and the basis functions used to represent the field within each element are the same used in the finite-element method. Element integration problems due to the singular kernel of the integral equations are treated in some detail. Numerical results for both the isotropic and the anisotropic spherical scatterer are presented, including comparisons with results obtained by different numerical methods for the isotropic cases considered. The capability of the numerical code presented here to deal with cases where the material parameters of the scatterer are given by singular matrices is discussed for two particular examples     

分段Padé逼近法用于预测二维介质柱的单站RCS方向图

矩量法与分段Pade逼近法结合用于预测任意形状截面二维介质柱的单站RCS方向图．该方法采用以总电场为未知函数的微积分方程．在矩量法过程中。用共轭梯度法和快速傅里叶变换(CG—FFT)的组合算法求解线性方程组，以便降低存储量和加快迭代速度．分段Pade逼近法用于加速获取单站RCS方向图．这里为分段Pade逼近法增添了一个自适应算法，克服了以往人工选择展开点位置的缺点．这种新的组合算法称为CG—FFT—PAIS算法．文中的数值算例证实了所述方法的有效性和实用性．     

3-D computation of E fields by the volume-surface integral equation(VSIE) method in comparison with the finite-integration theory (FIT)method [clinical hyperthermia application]

An algorithm has been developed for calculation of 3-D electric (E) fields by the volume-surface integral equation (VSIE) method. Integration over surface elements is performed using elementary analytical formulas, assuming a linear interpolation of surface charges. Grid points at electrical interfaces are split off, taking into account the E field behavior at these contours, specifically at sharp bends and multimedia junctions. Averaging procedures are utilized in order to avoid undefined or infinite values at critical points. The VSIE is solved by iteration using the GMRES (general minimum residuum) solver on a SUN workstation SPARC-IPX or Cray XMP, whereby convergence speed decreases considerably as the heterogeneity of the problem increases. Results for 3-D test cases (plane wave illuminating a layered cylinder) generally agree well with the finite-integration-theory (FIT) method if high E field gradients occur perpendicular to electrical boundaries. The VSIE method predicts slightly higher E fields only in critical regions. On the other hand, the FIT method at present is more efficient with respect to computation time for large domains with high cell numbers (>100000 cells)     

CFIE MM solution for TE and TM incidence on a 2-D conducting bodywith dielectric filled cavity

The problem of determining the scattering cross section of an arbitrarily shaped two-dimensional conducting body with an arbitrarily shaped dielectric filled cavity is considered. The problem is solved using a method-of-moments solution for the combined field integral equations. The particular form of the method of moments solution used here uses a minimum number of expansion coefficients. Results are given for transverse electric and transverse magnetic incident waves     

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.     

Theory of aperture-coupled hemispherical dielectric resonator antennas with radiating elements

A new approach based on hybrid volume-surface integral equation (VSIE) formulation in combination with spherical dyadic Green's function (DGF) is presented in this paper to analyze aperture-coupled multilayer hemispherical dielectric resonator antennas (DRA) with conformal conducting patches. Hybrid VSIE is used for the planar part of the structure and is solved with the aid of spatial-domain method of moments (MoM) in order to compute magnetic surface current in a slot cut in a finite planar perfect electric conductor (PEC) sheet. Multilayer spherical electromagnetic DGFs are used to compute loading effects of hemispherical dielectric resonators and conformal patches on antenna characteristics. The effects of variation in some parameters of the structure on the return loss of the antenna are studied. Accuracy of the presented method is validated by comparing the results obtained from the proposed method with those of CAD simulations.