Global numerical boundary condition based PDE solution techniquesfor open-region electromagnetic field problems

The underlying concept and algorithm for global numerical boundary condition (GNBC) based PDE solution techniques for open-region EMF problems are presented. This numerical procedure has been applied with success for various boundary-value problems in scattering, waveguide, and radiation analysis showing distinct advantages in generality, flexibility, and simplicity. All the GNBCs treated are of the first kind, i.e. eigenfunction-based GNBCs     

Numerically derived absorbing boundary condition for the solutionof open region scattering problems

An absorbing boundary condition is developed by means of a numerical approximation of the analytical behavior of the exact boundary condition. The boundary operator is more accurate than other analytically derived differential operators having the same order, and it can be applied to arbitrarily shaped scatterer geometries that can be handled most efficiently through the use of outer boundaries that conform to the body of the scatterer. Examples demonstrate the improvement in accuracy and efficiency achieved by the numerical boundary condition. The enhancement in accuracy is attributable to the inclusion of the evanescent harmonics behavior in the model     

分段积分共形算法在电磁散射问题中的应用

提出一种分段积分共形时域有限差分算法(PI-CFDTD),用于计算电磁散射问题。首先采用邻近网格电场场量插值表示变形网格中沿线电场场量,再以分段积分代替传统电场沿线积分求解,减小了阶梯误差,提高了电场环路积分的计算精度。推导出两种不同类型变形网格的电场环路积分公式,并对PI-CFDTD算法的稳定性进行研究,归纳得到应用原则。以金属方形平板和金属圆形平板作为算例进行验证,通过与传统时域有限差分法(FDTD)、传统共形时域有限差分法(CFDTD)以及矩量法(MoM)进行比较,表明PI-CFDTD计算精度更高。     

Three-dimensional biorthogonal multiresolution time-domain method and its application to electromagnetic scattering problems

A three-dimensional (3-D) multiresolution time-domain (MRTD) analysis is presented based on a biorthogonal-wavelet expansion, with application to electromagnetic-scattering problems. We employ the Cohen-Daubechies-Feauveau (CDF) biorthogonal wavelet basis, characterized by the maximum number of vanishing moments for a given support. We utilize wavelets and scaling functions of compact support, yielding update equations involving a small number of proximate field components. A detailed analysis is presented on algorithm implementation, with example numerical results compared to data computed via the conventional finite-difference time-domain (FDTD) method. It is demonstrated that for 3-D scattering problems the CDF-based MRTD often provides significant computational savings (in computer memory and run time) relative to FDTD, while retaining numerical accuracy.     

预条件共轭梯度法在辐射和散射问题中的应用

用矩量法求解一些辐射和散射问题 ,如线天线辐射和线状体散射等问题时 ,可以产生一个 Toeplitz线性方程组 ,采用预条件共轭梯度法 (PCG)与快速富里叶变换 (FFT)的结合方法 (PCGFFT)来求解该方程组 ,其中预条件器采用 T.Chan的优化循环预条件器。使用 PCGFFT算法 ,可有效地节省内存 ,提高了计算速度。为说明其有效性 ,将 PCGFFT算法与 CGFFT算法以及 Levinson递推算法进行了对比。     

A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach

A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. Past approaches involved applying a radiation condition at some distance from the scatterer in order to achieve a nearly reflection-free truncation of a finite-difference time-domain lattice. However, it is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic (TM) case, the integrand is known explicitly. For the transverse electric (TE) case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples areka = 5andka = 10. The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger thanka = 1. Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC. These will be the subject of a forthcoming paper.     

Matrix interpretation of the spectral iteration technique[electromagnetic scattering]

A matrix interpretation of the spectral iteration technique is presented to illustrate improvements in accuracy and convergence for both transverse magnetic and transverse electric waves incident on two-dimensional homogeneous scatterers producing solutions identical to a method of moments scheme. In this scheme, it is possible to improve the convergence rate of the technique by the use of nonphysical Green's function terms in the extended matrix. These terms result in the generation of a nonphysical field outside the scatterer, while still maintaining the correct solution of the current. Although the problem of nonconvergence has not been entirely overcome, a particular taper method used in the examples provided shows an improvement over their nontapered counterparts     

Convergence of the conjugate gradient method when applied to matrix equations representing electromagnetic scattering problems

An iterative procedure based on the conjugate gradient method is used to solve a variety of matrix equations representing electromagnetic scattering problems, in an attempt to characterize the typical rate of convergence of that method. It is found that this rate depends on the cell density per wavelength used in the discretization, the presence of symmetries in the solution, and the degree to which mixed cell sizes are used in the models. Assuming cell densities used in the discretization are in the range of ten per linear wavelength, the iterative algorithm typically requiresN/4toN/2steps to converge to necessary accuracy, whereNis the order of the matrix under consideration.     

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.     

Numerical solution of electromagnetic problems

Modern high-speed digital computers have made possible the solution, by theoretical-numerical techniques, of many problems in electromagnetics that have traditionally been solvable only by experimental methods. Formulated in terms of integral equations, the techniques described yield answers, with an accuracy and completeness unobtainable by experimental methods, in a small fraction of the time and at much less cost than by the experimental approach. Computer programs utilizing these techniques have been developed in the areas of radiation and scattering from arbitrary wire-antenna structures, bodies of revolution, and cylindrical bodies of arbitrary cross section.     

Application of Haar-wavelet-based multiresolution time-domainschemes to electromagnetic scattering problems

The multiresolution time-domain (MRTD) algorithm is applied to the problem of general two-dimensional electromagnetic scattering. A Haar wavelet expansion is utilized. A parallel between Haar MRTD and the classic Yee finite-difference time-domain (FDTD) algorithm is discussed, and results of simulations on canonical targets are shown for comparison. We focus on the incident-field implementation, which, in our case, consists of a pulsed plane wave. Also, we consider scattering in a half-space environment, with application to subsurface sensing. The results illustrate the advantage of the Haar MRTD method as compared with the classic FDTD, which consists of reduced memory and execution time requirements, without sacrificing accuracy     

Highly storage-efficient hybrid finite element/boundary element method for electromagnetic scattering

By properly choosing boundary surfaces and meshes of the hybrid finite element/boundary element method, one can reduce storage requirements of the boundary element matrices to the order of M for M boundary nodes.<>     

采用分部外推BCGS-FFT方法快速求解电磁散射问题

为了快速求解电磁散射问题中具有震荡性、奇异性、慢收敛性的索末菲积分,提出了一种利用分部外推算法加速索末菲尾部积分计算,并结合稳定双共轭快速傅里叶变换(stabilized biconjugate gradient fast Fourier transform,BCGS-FFT)算法求解电磁散射问题场分布情况的新方法. 首先给出电场积分方程(electric field integral equation, EFIE)的表达形式,且在求解过程的索末菲积分中应用一种便捷的椭圆积分路径来最小化索末菲积分的震荡性与奇异性,在索末菲尾部积分使用Levin分部外推法来提高积分收敛速度,以此来快速填充并矢格林函数矩阵. 然后对新方法进行了多种数值实验,验证算法的精确度,并对比了新方法与传统BCGS-FFT方法的计算效率,发现在保持相同计算精度的条件下,新方法可节省20%～37%的计算时间. 该方法能应用于复杂散射体嵌入多层空间的电磁散射计算,为快速求解目标区域的电磁散射场提供了一种新的方法.     

Use of the pattern equation method for solution of problems of scattering of electromagnetic waves by bodies covered with a dielectric

The pattern equation method is generalized to problems of scattering of electromagnetic waves by 3D perfectly conducting bodies covered with a dielectric. The method is implemented in an algorithm for bodies of a rather arbitrary shape. In the case of a sphere, explicit analytic expressions for the coefficients involved in the scattering pattern are obtained from the general system of equations for these coefficients. The expressions obtained coincide with the corresponding formulas in the theory of Mie series. Scattering patterns are calculated for various bodies of revolution. The calculation results for bodies with a coating are compared to similar characteristics obtained via simulation of a dielectric coating with the suitable impedance.     

Another method of extending the boundary condition for the problem of scattering by dielectric cylinders

Another method of extending the boundary condition resembling the extended boundary condition first developed by Waterman for the problem of scattering by homogeneous isotropic dielectric obstacles is presented. Differences between both methods are discussed from theoretical and numerical viewpoints.     

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.<>     

Reciprocity, discretization, and the numerical solution of directand inverse electromagnetic radiation and scattering problems

The author gives a formulation, based on Lorentz reciprocity, that unifies the finite element method (FEM) and the integral equation models. Wave propagation and scattering problems in electromagnetics have to be addressed with the aid of numerical techniques. Many of these methods can be envisaged as being discretized versions of appropriate weak formulations of the pertinent operator (differential or integral) equations. For the relevant problems as formulated in the time Laplace-transform domain it is shown that the Lorentz reciprocity theorem encompasses all known weak formulations, while its discretization leads to the discretized forms of the corresponding operator equations, in particular to their finite-element and integral-equation modeling schemes. Both direct (forward) and inverse problems are discussed     

二维散射问题的一个完整的时域解

本文研究了利用卷积直接求解瞬态散射远场的方法，得到二维散射问题完整的时域解，通过计算实例与严格理论解的比较，表明算法的正确性，评议中给出几种规则散射体的RCS和瞬态散射远场的计算结果。     

基于频域广义传输矩阵方法的电磁散射特性分析

多尺度复杂电子系统的电磁场问题难以用单一的计算电磁学方法进行高效数值计算.基于区域分解方法和惠更斯等效原理，提出了频域广义传输矩阵（generalized transition matrix，GTM）方法:将系统分解为多个子模块，通过电场积分方程（electric field integreal equation，EFIE）把各个子模块的电磁特性进行提炼，再考虑所有子模块之间的电磁耦合，计算系统整体电磁场分布.GTM方法把多尺度问题转化为尺度相对比较单一的问题进行处理，在分析各种复合结构、非均匀各向异性介质、大型相控阵天线等电磁散射特性时，提供了灵活的解决方案.论文给出了GTM在手征介质、开口腔体以及Vivaldi相控阵天线电磁特性分析中的应用算例，当未知量个数压缩到原来的十分之一时，GTM计算结果与直接用矩量法（methed of moment，MoM）求解的计算结果非常吻合.GTM可以简洁地表示目标问题的电磁散射特征，与传统MoM相比，大幅度减少了基函数的数量，具有较高的计算精度和效率.     

A hybrid method for combining quasi-static and full-wave techniquesfor electromagnetic scattering problems

Electromagnetic scattering problems containing subregions which are electrically small but geometrically complex are examined. By utilizing quasi-static methods for the small regions, full-wave methods in the remaining region, and determining necessary coupling relations between the small regions and the overall geometry, a considerable improvement in numerical efficiency is realized. The particular method developed here is valid for quasi-static regions in which magnetic induction can be ignored. Results using the proposed method have been obtained for a pair of closely spaced collinear wires. A comparison of these results with the wire antenna code, MININEC, showed excellent agreement