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     

High-order generalized extended Born approximation for electromagnetic scattering

Previous work on the subject of electromagnetic scattering has shown that the extended Born approximation (EBA) is more accurate than the first-order Born approximation with approximately the same operation count. However, the accuracy of the EBA degrades in cases when the source is very close to the scatterer, or when the electric field exhibits significant spatial variations within the scatterer. This paper introduces a generalized extended Born approximation (GEBA) and its high-order variants (Ho-GEBA) to efficiently and accurately simulate electromagnetic scattering problems. We make use of a generalized series expansion of the internal electric field to construct high-order terms of the generalized extended Born approximation (Ho-GEBA). A salient feature of the Ho-GEBA is its enhanced accuracy over the Born approximation and the EBA, even when only the first-order term of the series expansion is considered in the approximation. This behavior is not conditioned by either the source location or the spatial distribution of the internal electric field. A unique feature of the Ho-GEBA is that it can be used to simulate electromagnetic scattering due to electrically anisotropic media. Such a feature is not possible with approximations of the internal electric field that are based on the behavior of the background electric field. Three-dimensional (3-D) models of electromagnetic scattering are used to benchmark the efficiency and accuracy of the Ho-GEBA, including comparisons against the first-order Born approximation and the EBA.     

A finite-difference time-domain near zone to far zonetransformation [electromagnetic scattering]

An efficient time-domain near-zone-to-far-zone transformation for FDTD (finite-difference-time-domain) computations is presented. The approach is to keep a running accumulation of the far-zone time-domain vector potentials due to the tangential electric and magnetic fields on a closed surface surrounding the scatterer at each time step. At the end of the computation, these vector potentials are converted to time-domain far-zone fields. Many far-zone bistatic directions can be included efficiently during one FDTD computational run. Frequency domain results can be obtained via fast Fourier transform. Wideband results for scattering from a perfectly conducting plate were obtained from a single FDTD computation transformed to the frequency domain, and compared with moment method results. This approach is significantly more efficient than computing many FDTD results using sinusoidally varying excitation if a wide frequency band is of interest. Coupled with recent advances in computing FDTD results for frequency-dependent materials, wideband results for far-zone scattering from targets including frequency-dependent materials can be obtained efficiently     

Coupling finite element and integral equation solutions usingdecoupled boundary meshes [electromagnetic scattering]

A method is outlined for calculating scattered fields from inhomogeneous penetrable objects using a coupled finite element-integral equation solution. The finite element equation can efficiently model fields in penetrable and inhomogeneous regions, while the integral equation exactly models fields on the finite element mesh boundary and in the exterior region. By decoupling the interior finite element and exterior integral equation meshes, considerable flexibility is found in both the number of field expansion points as well as their density. Only the nonmetal portions of the object need be modeled using a finite element expansion; exterior perfect conducting surfaces are modeled using an integral equation with a single unknown field since E _tan is identically zero on these surfaces. Numerical convergence, accuracy, and stability at interior resonant frequencies are studied in detail     

Treating the instabilities in marching-on-in-time method from adifferent perspective [electromagnetic scattering]

A general method is presented to treat the instabilities which are frequently observed in the electromagnetic transient solutions using the marching-on-in-time method. The basic idea is to apply an finite impulse response (FIR) filter with a constant group delay during the course of marching-in-time. An electric field integral equation (EFIE) formulation for perfectly conducting bodies is used as a vessel to demonstrate the method. Sample numerical results are presented and discussed. The computed results, while showing good agreement with the data obtained from other methods, present great stability improvement     

On the sharpness of a needle [electromagnetic propagation]

In a recent paper [Oct. 2003], Van Bladel discussed in detail the behavior of fields and surface charges near singularities of metallic structures, such as a hollow circular cylinder, a circular cone, a thin prolate spheroid, and a uniformly charged segment. At times, the reasoning in [Van Bladel, Oct. 2003] leads to conclusions not as definitive as one might wish because of the various approximations introduced, such as the electrostatic limit for the field or idealized singularities for the conductors (e.g., the tip of a cone). In this work, an example is provided that may assist in shedding some light on the questions raised in [Van Bladel, Oct. 2003], because it consists of an exact, closed-form, simple solution to a boundary-value problem that is valid at all frequencies. The problem consists of a plane wave propagating in free space and axially incident on the convex side of a paraboloid of revolution. This problem was solved by Schensted [1955] for a perfectly conducting (PEC) paraboloid, and by Roy and Uslenghi [Oct. 1997] for an isorefractive paraboloid, which comprises the PEC paraboloid as a particular case. A remarkable fact is that these exact solutions are also the geometrical optics solutions.     

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.     

Technique for mechanical measurements using optical scattering froma micropipette [cells application]

The authors propose an optical method using forward light scattering to measure the deflection of a micropipette from a normal contact force with a small elastic solid, and the damping coefficient of a small fluid sample through a dynamic interaction with the pipette. An analytical and experimental study of this sensor is performed and described for each property. Topics covered include: (1) forward light scattering technique for determining the diameter of a micropipette (using exact and simplified geometric interference theories); (2) deflection measurement and analysis on the pipette-sample system using the finite element method; and (3) equivalent damping coefficient and resonant frequency measurement of the pipette-fluid system and its numerical solution derived from the finite element model. A comparison of the experimental results and the analytical results is included to provide the means for analyzing the potential of this new method     

Implementation and application of resistive sheet boundarycondition in the finite-difference time-domain method [EM scattering]

Use of a resistive sheet boundary condition in the finite-difference-time-domain (FDTD) analysis of scattering problems involving a resistively coated dielectric object is described. An algorithm is introduced through an analysis of E-polarized scattering from a thin resistive strip. For a given resistance, numerical experiments indicate that algorithm stability is ensured for time sampling intervals chosen according to a specific criterion. Validity of the resultant FDTD method is verified in a comparison of computed E-polarized scattering data for several resistive strips with existing data. Results on the E-polarized scattering behaviour of a resistively coated dielectric strip as a function of surface resistances and angle of incidence are also presented. Extension to the H-polarized case and application of the present method to pulsed problems are briefly discussed     

EM Programmer's Notebook [EM scattering]

An interactive circular-cylinder modeler software program in which the approximation of a complex scatterer is achieved by using circular cylinders is described. The cylinders are made of either homogeneous isotropic dielectric material, perfectly conducting material characterized by a surface impedance, or a combination of the two. The user interface is designed for quick construction of two-dimensional scatterers using circular cylinders of arbitrary radii. The algorithm for multiple scattering between these cylinders is based on the enforcement of the appropriate boundary conditions on the surface of each cylinder. The source of excitation can be a plane wave or a line source parallel to the scatterer, and both TM and TE types of polarization are considered     

Analysis of a parallel resistive plate medium [EM scattering]

A half-space composed of parallel resistive sheets is studied by formulating an eigenvalue problem to find the characteristic modes of the medium. Two equivalent formulations of the eigenvalue problem are presented. The first approach is analytical in nature and provides greater insight into the physical behavior of the material, while the second is numerical and applicable to a wider class of problems. The eigenvalue problem is solved via the Muller method to find the complex modal wavenumbers and field distributions within the resistive sheet medium. The mode-matching procedure is used to study the medium's reflection and absorption properties     

Numerically efficient solution of dense linear system of equationsarising in a class of electromagnetic scattering problems

In this paper we present an efficient technique for solving a dense complex-symmetric linear system of equations arising in the method of moments (MoM) formulation. To illustrate the application of the method, we consider a finite array of scatterers, which gives rise to a large number of unknowns. The solution procedure utilizes preconditioned transpose-free QMR (PTFQMR) iterations and computes the matrix-vector products by employing a compressed impedance matrix. The compression is achieved by reduced-rank representation of the off-diagonal blocks, based on a partial-QR decomposition, which is followed by an iterative refinement. Both the preconditioning and the compression steps take advantage of the block structure of the matrix. The convergence of the iterative procedure is investigated and the performance of the proposed algorithm is compared to that achieved by other schemes. The effectiveness of the preconditioner and the degree of matrix compression are quantified. Finite arrays of variable shape and sizes are considered, and it is demonstrated that the ability to solve large problems using this technique enables one to evaluate the edge effects in the finite array. Such array is basically flat and periodic, but the algorithm is still efficient when variation with strict periodicity or flatness exists     

面向工程应用的电磁散射特性建模关键问题研究

随着计算电磁学和计算机技术的迅速发展，电磁散射特性建模技术从算法研究向产品化、集成化、工程化发展.文中分析了探测、识别、伪装等实际工程应用中对电磁散射特性建模技术的具体需求，总结了几何建模、网格剖分、电磁计算和模型验证等建模流程中存在的关键问题与解决方式，以及电磁散射建模技术的发展特点.     

Finite element computation of electromagnetic fields [hyperthermiatreatment]

A three dimensional finite element solution scheme is developed for numerically computing electromagnetically induced power depositions. The solution method is applicable to those problems for which it can be reasonably assumed that the magnetic permeability is homogeneous. The method employs an incident field/scattered field approach where the incident field is precalculated and used as the forcing function for the computation of the scattered field. A physically logical condition is used for the numerical boundary conditions to overcome the fact that electromagnetic problems are generally unbounded (i.e., the boundary condition is applied at infinity) but numerical models must have a boundary condition applied to some finite location. At that numerical boundary, an outgoing spherical wave is simulated. Finally, an alternate to a direct solution scheme is described. This alternate method, a preconditioned conjugate gradient solver, provides both a storage and CPU time advantage over direct solution methods. For example, a one-thousand fold decrease in CPU time was achieved for simple test cases. Unlike most iterative methods, the preconditioned conjugate gradient technique used has the important property of guaranteed convergence. Solutions obtained from this finite element method are compared to analytic solutions demonstrating that the solution method is second-order accurate     

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.     

Analyzing low-frequency electromagnetic scattering from a compositeobject

In this paper, we present a method for solving electromagnetic scattering from a composite object at low frequencies using the method of moments (MoM) and loop-tree basis. Many applications involve composite objects which consist of several homogeneous regions. The loop-tree basis used for analyzing scattering from a homogeneous body at low frequencies could not be directly applied to analyze the low-frequency scattering from a composite object. In general, it is very difficult, if not impossible, to find a set of loop-tree basis functions that is valid for the structures on both sides of the interfaces. In this paper, we treat a composite object as a limiting case of multibody problem so that we could setup the MoM equation using the loop-tree basis found on each single body. A process is then developed to eliminate the redundant unknowns. The proposed method makes it possible to analyze low-frequency scattering from an arbitrary composite object. The validity and applications are illustrated with representative numerical examples     

The application of contraction theory to an iterative formulation of electromagnetic scattering

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (ork-space) formulation is presented with an emphasis on application to periodic surfaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.     

Generalized scattering matrix of generalized two-portdiscontinuities: application to four-port and nonsymmetric six-portcouplers

A field theory analysis of multiport, multidiscontinuity structures based on the generalized scattering matrix (GSM) of a generalized two-port discontinuity concept is presented. The analysis can be used in any structure equipped with any number of input and output ports, and results in substantial simplifications over previous analyses. The GSMs of generalized two-port discontinuities can also be cascaded with the same procedure as the two-port discontinuities and can be used to determine the electromagnetic field and the Poynting vector at every point of the structure. The GSM of the generalized two-port technique is used to analyze four-port and nonsymmetric six-port branch-waveguide directional couplers, and good agreement between the theoretical results and experimental data is obtained     

A generalized scattering matrix method using the method of momentsfor electromagnetic analysis of multilayered structures inwaveguide

The method of moments (MoM) in conjunction with the generalized scattering matrix (GSM) approach is proposed to analyze transverse multilayered structures in a metal waveguide. The formulation incorporates ports as an integral part of the GSM formulation, thus, the resulting model can be integrated with circuit analysis. The proposed technique permits the modeling of interactive discontinuities due to the consideration of a large number of modes in the cascade. The GSM-MoM method can be successfully applied to the investigation of a variety of shielded multilayered structures, iris coupled filters, determining the input impedance of probe excited waveguides, and of waveguide-based spatial power combiners