A three-dimensional iterative scheme for an electromagneticcapacitive applicator

An efficient iterative method for solving quasi-static electromagnetic field problems is presented. A relaxation function is introduced in the quasi-static field equations. Then, the resulting equations can be solved by iteration. The method is similar to the one of solving a Laplace equation by computing the stationary state of a diffusion equation. Next, for a radially layered configuration the numerical results are compared with the results from an existing integral equation method. Subsequently, for a realistic three-dimensional model of a human knee numerical results are arrived at.     

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.     

Iterative computational techniques in scattering based upon the integrated square error criterion

An iterative technique is developed to rigorously compute the electromagnetic time- and frequency-domain scattering problems. The method is based upon a wave-function expansion technique (this also includes the integral-representation techniques), in which the electromagnetic field equations and causality conditions are satisfied analytically, while the boundary conditions or the constitutive relations have to be satisfied in a computational manner. The latter is accomplished by an iterative minimization of the integrated square error. For the solution of an integral equation, it is shown how to obtain optimum convergence. Some numerical results pertaining to a number of representative problems illustrate the numerical advantages and disadvantages of the iterative method.     

Adaptive multiscale moment method (AMMM) for analysis of scatteringfrom perfectly conducting plates

Adaptive multiscale moment method (AMMM) is presented for the analysis of scattering from a thin perfectly conducting plate. This algorithm employs the conventional moment method and a special matrix transformation, which is derived from the tensor products of the two one-dimensional (1-D) multiscale triangular basis functions that are used for expansion and testing functions in the conventional moment method. The special feature of these new basis functions introduced through this transformation is that they are orthogonal at the same scale except at the initial scale and not between scales. From one scale to another scale, the initial estimate for the solution can be predicted using this multiscale technique. Hence, the compression is applied directly to the solution and the size of the linear equations to be solved is reduced, thereby improving the efficiency of the conventional moment method. The basic difference between this methodology and the other techniques that have been presented so far is that we apply the compression not to the impedance matrix, but to the solution itself directly using an iterative solution methodology. The extrapolated results at the higher scale thus provide a good initial guess for the iterative method. Typically, when the number of unknowns exceeds a few thousand unknowns, the matrix solution time exceeds generally the matrix fill time. Hence, the goal of this method is directed in solving electrically larger problems, where the matrix solution time is of concern. Two numerical results are presented, which demonstrate that the AMMM is a useful method to analyze scattering from perfectly conducting plates     

Unified theory of near-field analysis and measurement: Scattering and inverse scattering

The many scanning procedures of the author's unified theory of near-field analysis and measurement are applied to the determination of complex bistatic scattering patterns of scalar and electromagnetic systems, both with and without correction for the patterns of the probes, one of which may be a compact range. For high accuracy, both the incident and scattered fields are expressed as linear combinations of exact solutions of the differential equations involved (Maxwell's in the electromagnetic cases). For high efficiency, natural orthogonalities with respect to summation are used to decouple the simultaneous equations expressing the measurements in terms of the desired pattern coefficients, implemented by the highly efficient fast Fourier transform as an approximation-free symmetry decomposition. The scanning procedures include spherical, a new, more accurate, more efficient type of plane polar, and many types of plane rectangular, plane radial, and circular cylindrical. All these results are expressed with a single notation and generally applicable equations, based upon symmetry analysis and relativistic invariances. The full apparatus of group representations is applied to reducing the measurement and computational effort, determining symmetries from scattering patterns, and determining Garbacz and singularity expansion method (SEM) modes. Further, Snell's laws, Fresnel's law, and conservation of momenta (e.g., propagation constants) are explained in terms of relativistic invariances.     

A near-field preconditioner and its performance in conjunction with the BiCGstab(ell) solver

This paper describes a simple physically-motivated "near-field" preconditioning scheme that is effective in accelerating convergence of surface, volume, and combined surface/volume integral equations for a broad variety of electromagnetic scattering problems. It can be easily implemented numerically in method of moment (MoM) solvers (both conventional and those employing matrix-compression techniques), irrespective of the analytical form of the integral-equation kernel. It has low memory and CPU requirements, both of which scale linearly with the number of unknowns, and is easily amenable to efficient parallelization. We demonstrate the preconditioner's performance (in conjunction with the BiCGstab(ell) iterative solver) on two representative geometries, and observe a significant reduction in the number of iterations required for convergence.     

隐身目标的P 波段电磁散射特性仿真研究

介绍了敌方隐身目标的威胁、P 波段反隐身的基本原理及该频段电磁散射特性的研究现状,分析了基于快速多极子技术的全波数值仿真方法在隐身目标散射特性精确求解中的独特作用;阐释了基于快速多极子技术的全波数值仿真方案实施的矩量法原理、快速多极子技术、预处理算法及高效迭代求解技术,通过与标准体的测量结果对比,验证了仿真方案的可靠性及精度;利用文中提出的仿真框架对几种典型的隐身目标进行数值仿真,讨论了隐身目标在P 波段的电磁散射特性。     

Scattering from periodic strip gratings via the secant-spectraliterative method

The secant method is used in an iterative algorithm for calculating the electromagnetic scattering from planar, periodic gratings. Results are compared with the moment method and the contraction-corrector spectral-iteration technique (SIT) methods. The secant approach does not depend on the evaluation of numerical derivatives to achieve convergence like the contraction-corrector SIT method. Suggestions for applying this method to more complicated structures are included     

基于阻抗边界条件建模的涂敷目标电磁散射分析

针对飞行器上常用的涂敷吸波材料结构开展电磁散射数值建模和散射特性分析。利用涂敷结构表面电磁场的阻抗边界条件,建立表面电流和表面磁流的新型积分方程形式,并利用快速算法进行求解。数值结果表明:该型积分方程在不增加额外计算量和存储量的条件下,显著改善了迭代求解收敛性,为复杂涂敷结构的电磁散射分析提供了快速、可靠的技术途径。     

An iterative method of solving a system of linear equations and its physical interpretation from the point of view of scattering theory

The iterative method is useful to find the approximate solution of large systems of linear equations when the exact method becomes too expensive to be implemented. One well-known iterative method is the Gauss-Seidel method. The author presents an alternative algorithm which has certain simplicity in its formulation. He uses the system of linear equations encountered in the theory of coupled antennas to illustrate this method and give a physical interpretation of the successive approximations from the point of view of scattering theory. A simple numerical example is given to compare the products resulting from this method and those obtained by the Gauss-Seidel method     

Scale-Space Properties of Nonstationary Iterative Regularization Methods

Most scale-space concepts have been expressed as parabolic or hyperbolic partial differential equations (PDEs). In this paper we extend our work on scale-space properties of elliptic PDEs arising from regularization methods: we study linear and nonlinear regularization methods that are applied iteratively and with different regularization parameters. For these so-called nonstationary iterative regularization techniques we clarify their relations to both isotropic diffusion filters with a scalar-valued diffusivity and anisotropic diffusion filters with a diffusion tensor. We establish scale-space properties for iterative regularization methods that are in complete accordance with those for diffusion filtering. In particular, we show that nonstationary iterative regularization satisfies a causality property in terms of a maximum–minimum principle, possesses a large class of Lyapunov functionals, and converges to a constant image as the regularization parameters tend to infinity. We also establish continuous dependence of the result with respect to the sequence of regularization parameters. Numerical experiments in two and three space dimensions are presented that illustrate the scale-space behavior of regularization methods.     

Adaptive multiscale moment method (AMMM) for analysis of scatteringfrom three-dimensional perfectly conducting structures

The adaptive multiscale moment method (AMMM) is presented for the analysis of scattering from three-dimensional (3D) perfectly conducting bodies. This algorithm employs the conventional moment method (MM) using the subsectional triangular patch basis functions and a special matrix transformation, which is derived from solving the Fredholm equation of the first kind by the multiscale technique. This methodology is more suitable for problems where the matrix solution time is much greater than the matrix fill time. The widely used triangular patch vector basis functions developed by Rao et al., (1982), are used for expansion and testing functions in the conventional MM. The objective here is to compress the unknowns in existing MM codes, which solves for the currents crossing the edges of the triangular patch basis functions. By use of a matrix transformation, the currents, source terms, and impedance matrix can be arranged in the form of different scales. From one scale to another scale, the initial guess for the solution can be predicted according to the properties of the multiscale technique. AMMM can reduce automatically the size of the linear equations so as to improve the efficiency of the conventional MM. The basic difference between this methodology and the other wavelet-based techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly in an iterative fashion even though it is an unknown. Two numerical results are presented, which demonstrate that the AMMM is a useful method for analysis of electromagnetic scattering from arbitrary shaped 3D perfectly conducting bodies     

Study of a self-consistent pulsed electron flow in an irregular waveguide

A mathematical model is presented for self-consistent interaction of pulsed electron flows with the electromagnetic waves they excite in irregular waveguides. The model is applied to axially symmetric systems and based on simultaneous solution of an inhomogeneous system of nonstationary waveguide equations and relativistic equations of motion of a system of quasi-particles that approximate the electron flow. Results of calculations are presented for the case of a pulse of photoelectrons emitted from the walls of a hyperboloid of revolution. The flow is accelerated preliminarily by means of a grid that has a high transmission factor.     

Preconditioning of electromagnetic integral equations usingpre-defined wavelet packet basis

A preconditioner based on the pre-defined wavelet packet (PWP) basis is proposed to accelerate the convergence of iterative solvers for large-scale electromagnetic scattering problems. With the moment equations more efficiently represented using the wavelet packet bases, an effective block-diagonal preconditioner can be constructed. Simulation results show that the convergence rate for inlet-type scatterers can be significantly improved while maintaining a moderate computation cost for the preconditioning operation     

A hybrid BEM/WTM approach for analysis of the EM scattering fromlarge open-ended cavities

An effective hybrid boundary-element method (BEM) and wavelet-transform method (WTM) is proposed to analyze electromagnetic scattering from three-dimensional (3-D) open-ended cavities with arbitrary shapes. This hybrid technique formulates the original cavity problems by a magnetic field integral equation. The BEM is employed to establish the mapping between the original complex integral surface and the unit square. The WTM is used to reduce the density of the moment matrix. Since a surface integral equation has to be solved, the WTM requires a two-dimensional (2-D) wavelet basis to implement the numerical computation. The previous fast iterative algorithm for 2-D wavelets has been extended for efficiently constructing various 2-D wavelet basis functions by a tensorial product from two one-dimensional (1-D) regular multiresolution analyses. Unlike the conventional method of moments, the proposed hybrid technique can always obtain sparse moment matrix equations, which can be efficiently solved by sparse solvers. As the level scales for numerical discretization of cavities increase, larger compression rates can be obtained, which makes it possible for the hybrid BEM/WTM technique to efficiently solve scattering from large open-ended cavities with complex terminations. Numerical results are presented to demonstrate the merits of the proposed method     

Improved numerical diffraction coefficients with application tofrequency-selective surfaces

A method for numerically determining diffraction coefficients for arbitrary scattering centers is described. In this method finite bodies possessing scattering centers of the type of interest are first analyzed via the moment method. The various contributions to the total scattered fields are then isolated by solving low-order simultaneous equations obtained by writing expressions for the fields in terms of unknown diffraction coefficients. The method yields numerical diffraction coefficients in angular sectors where previous methods fail (e.g., near grazing angles), and can be applied in the context of measured as well as simulated scattering data. Finite frequency-selective surfaces are shown to be amenable to analysis with ray-optics techniques, and several two-dimensional examples are given with comparisons to far- and near-field moment method results     

Spurious fields in time-domain computations of scattering problems

Two-dimensional (2-D) electromagnetic scattering problems with a time-periodic incident field are considered. The scatterer is a perfect conductor, and an artificial boundary condition is used. The large-time behavior of solutions, depending on (divergence-free) initial conditions, is characterized. It turns out that in addition to the expected time-periodic solution, the limiting solution may also contain a spurious stationary field. The source of the stationary field is explained and equations describing it are obtained. Several avoidance strategies are discussed and numerical comparisons of these techniques are given     

周期小波在电磁散射中的应用

讨论周期小波与矩量法相结合的方法在二维电磁散射计算中的应用，以周期小波作为基函数和权函数，并利用ｃｏｉｆｌｅｔ小波的消失矩性质，求解速度较快，结果非常精确。本文分别用小波矩量法、传统的矩量法及广义多极子方法计算了一个无限长方柱在平面波照射下的电流分布，并与有关资料上的结果进行比较，吻合得很好。     

A multilevel matrix decomposition algorithm for analyzingscattering from large structures

A multilevel algorithm is presented for analyzing scattering from electrically large surfaces. The algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics. The algorithm permits a fast matrix-vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks, with each describing the interaction between distant scatterers. The multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast Fourier transform (FFT) and that only relies on well-known algebraic techniques. The computational complexity and the memory requirements of the proposed algorithm are O(N log² N)     

On the use of spatio-temporal multiresolution analysis in method ofmoments solutions of transient electromagnetic scattering

A novel method of moments approach to the solution of time-domain integral-equation formulation of electromagnetic scattering problems is presented. The method is based on a spatio-temporal multiresolution analysis. This analysis facilitates a basis from which a small number of expansion functions is selected via an iterative procedure and utilized to model the unknown current distribution. In contrast to marching-on-in-time sequential procedures, the proposed method models the unknown current simultaneously at all the time steps within the time frame of interest. This new method is applied to a one-dimensional (1-D) problem of electromagnetic plane wave interaction with a dielectric slab. A comparison of the computed results with results based on the analytic solution demonstrates that the method is capable of attaining accurate results while achieving substantial reduction in computation time and resources