Comparison of linear and quadratic hexahedral edge elements in electromagnetic scattering problems

In this article, performances of linear and quadratic hexahedral edge elements are compared in the context of electromagnetic scattering problems. The de-facto standard of 0.1λ element size for linear elements is taken as a basis; and 0.3 to 0.4λ-size quadratic element usage is proposed for a better accuracy level with dramatic reduction in computation time and memory. The proposed scheme is applied to some well-known practical problems.     

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.     

Rapid solution of parameter-dependent linear systems for electromagnetic problems in the frequency domain

The minimal residual interpolation method reduces the number of iterations in an iterative method for multiple right-hand sides. It uses computed solutions to initialize an iterative solver with an accurate guess. This work demonstrates the efficiency of the method for frequency sweeps and solving scattering problems by plane waves incident from multiple angles. A bound on the number of solutions required for plane wave scattering before the remaining solutions obtained by minimal residual interpolation only is given. We discuss the performance of the method compared to iterative seed techniques. In a numerical example, a reduction factor of 60 is obtained on the number of matrix vector multiplications.     

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.     

Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces

Simple and efficient numerical methods are developed for treating electromagnetic problems of scattering and radiation from surfaces. Special consideration is given to the treatment of edges so that rather arbitrary geometrical configurations may be handled. For the conducting body problems considered, an electric field integral formulation is used, and the method of moments is applied using pulse expansions to represent both the current and the charge. It is demonstrated that proper placement of the current and charge subdomains relative to edges not only is important in treating edges but also yields a convenient numerical procedure. A simple testing scheme is used which is almost as efficient as point-matching. Numerical results indicate that the approach is free of anomalies in the behavior of current near edges and of other previously observed numerical instabilities. Problems considered include conducting strips (both TM and TE), a bent rectangular plate, and both material and conducting bodies of revolution.     

基于改进的体面积分方程区域分解方法高效求解有限大频率选择表面结构的电磁散射特性

针对复杂的有限大频率选择表面（frequency selective surface，FSS）结构阐述了一种改进的非重叠和非共型的体面积分方程区域分解方法（volume-surface integral equation domain decomposition method，VSIE-DDM）.为了对其进行高效的电磁分析，我们在最近发展的VSIE-DDM的基础上开发了不同的分区方式，每个子区域不必相同大小，可以任意形状，使该VSIE-DDM分区更加灵活.并且由于FSS的精细单元和薄介质基底，导致网格比较稠密，因此得到维度比较大的矩阵.为了更高效计算更大维度的子区自耦合矩阵的逆，使用了内外迭代技术使得该方法可以采用电尺寸更大的子区，获得更好的收敛性，进一步提高了仿真效率.通过几个数值算例验证了本文所提算法的计算性能.     

Finite-element solution to electromagnetic scattering problems bymeans of the Robin boundary condition iteration method

A new numerical method, called the Robin boundary condition iteration (RBCI), is proposed for the finite-element (FE) solution of electromagnetic scattering problems in open boundary domains. The unbounded domain is truncated to a bounded one by means of a fictitious boundary that contains the scatterer and on which a suitable nonhomogeneous Robin (mixed) boundary condition is assumed for the Helmholtz equation in the bounded domain. The Robin condition is expressed by means of an integral formula (the second Green identity) in terms of the field in the interior of the bounded domain, with the integration surface being a surface strictly enclosed by the truncation boundary. The discretized differential and integral equations are then coupled together to solve the problem. The formulation is completely immune from the well-known interior resonance problems. A simple and effective iterative solving scheme is described. Examples are also provided to validate RBCI and compare it with other methods     

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.<>     

Solution of electromagnetic scattering problems using time domaintechniques

New method are developed to calculate the electromagnetic diffraction or scattering characteristics of objects of arbitrary material and shape. The methods extend the efforts of previous researchers in the use of finite-difference and pulse response techniques. Examples are given of the scattering from infinite conducting and nonconducting cylinders, open channel, sphere, cone, cone sphere, coated disk, open boxes, and open and closed finite cylinders with axially incident waves     

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     

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     

Survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems

Many of the popular methods for the solution of large matrix equations are surveyed with the hope of finding an efficient method suitable for both electromagnetic scattering and radiation problems and system identification problems.     

Transverse scattering matrix formulation for a class of waveguideeigenvalue problems

Based on the mode-matching procedure, a unified transverse scattering matrix formulation is presented for the characterization of a class of waveguide eigenvalue problems, which include not only closed but also open structures. As examples, calculations are carried out on the dispersion characteristics of ridged waveguides and their variations, nonradiative dielectric (NRD) waveguides, groove guides, microstrip lines, finlines and coplanar waveguides. Comparisons with published data are made and verify the versatility and accuracy of the method. Besides its generality, this approach is also superior to some other techniques in simplicity and numerical efficiency     

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     

An efficient solution of a class of integrals arising in antenna theory

A novel analytical solution for a class of power-radiation integrals, arising in antenna theory, is presented. These integrals are then applied to the analysis of circular-loop and circular-microstrip antennas, and the results are compared to published results obtained using numerical integration. The analytical solution is shown to be sufficiently accurate and efficient for the calculation of the radiation characteristics of these types of antennas. Possible applications to other types of antennas are discussed.     

UTD solution for electromagnetic scattering by a circular cylinderwith thin lossy coatings

A uniform geometrical theory of diffraction (UTD) solution is obtained for the field exterior to a two-dimensional circular cylinder with a thin lossy dielectric coating. The solution is convenient for engineering applications due to its simple ray format. In the lit region, the geometrical optics (GO) solution consists of the direct incident ray and the reflected ray. In the shadow region, the geometrical theory of diffraction (GTD) uses the creeping-wave format to calculate the diffracted field. In the transition regions adjacent to the shadow boundaries, where the pure ray optical solution fails, a `universal' transition integral is used for the UTD solution to calculate the field. Numerical values for the essential transition integral are deduced, by a heuristic approach, from alternative representations of the Green's function for a circular cylinder with coating. Numerical results obtained from the UTD solution show excellent agreement with the eigenfunction results for cylinders with thin dielectric coatings     

Boundary integrodifferential equations for electromagnetic scattering problems in three dimensions

On the basis of two vector representations of electromagnetic fields we introduce a new system of boundary integrodifferential equations for the solution of scattering problems in three dimensions. The unknowns of this system present two scalar functions, namely, the "" coefficients of Atkinson-Wilcox expansion; electromagnetic field being reconstructed with these functions by means of certain recursive-differential operators. We define an algebraic analog of the equations by expanding unknowns into Fourier series with respect to spherical harmonics. Verification of the approach is done on the basis of the solution of well-known canonical problems.     

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.     

Derivation and application of a class of generalized boundaryconditions [electromagnetic scattering]

Boundary conditions involving higher order derivatives are presented for simulating surfaces whose reflection coefficients are known analytically, numerically, or experimentally. Procedures for determining the coefficients of the derivatives are discussed, along with the effect of displacing the surface where the boundary conditions are applied. Provided the coefficients satisfy a duality relation, equivalent forms of the boundary conditions involving tangential field components are deduced, and these provide the natural extension to nonplanar surfaces. As an illustration, a metal-backed uniform dielectric layer is simulated. It is shown that fourth-order conditions are capable of providing an accurate simulation for layers at least a quarter of a wavelength in thickness     

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。