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     

Hybrid solutions for large-impedance coated bodies of revolution

Electromagnetic scattering solutions are developed for coated perfectly conducting bodies of revolution (BOR) that satisfy the impedance boundary condition. The integral equation arising from the impedance (Leontovich) boundary condition is solved by use of the method of moments (MM) technique along with an Ansatz for the surface currents that is derived from physical optics (PO) and the Fock theory that is modified for imperfectly conducting surfaces. The MM solution is expressed in terms of two integral (Galerkin) operators. The form of the Galerkin expansion used results in a symmetric MM system matrix. The hybrid solution is specialized for BOR's although the approach is applicable to a broader class of scatterers as well. The results are compared with the Mie solution for penetrable spherical scatterers, which satisfy the impedance boundary condition, and with recently published MM solutions for nonspherical scatterers.     

TM scattering by an impedance sheet extension of a paraboliccylinder

An integral equation and method of moments (MM) solution are presented for the two-dimensional (2-D) problem of transverse magnetic (TM) scattering by an impedance-sheet extension of a perfectly conducting parabolic cylinder. An integral equation is formulated for a dielectric cylinder of general cross section in the presence of a perfectly conducting parabolic cylinder. It is then shown that the solution for a general dielectric cylinder considerably simplifies for the special case of TM scattering by a thin multilayered dielectric strip that can be represented as an impedance sheet. The solution is termed an MM/Green's function solution, where the unknowns in the integral equation are the electric surface currents flowing in the impedance sheet; the presence of the parabolic cylinder is accounted for by including its Green's function in the kernel of the integral equation. The MM solution is briefly reviewed, and expressions for the elements in the matrix equation and the scattered fields are given. Sample numerical results are provided     

Integral equation formulations for imperfectly conducting scatterers

Integral equation formulations are presented for characterizing the electromagnetic (EM) scattering interaction for nonmetallic surfaced bodies. Three different boundary conditions are considered for the surfaces: namely, the impedance (Leontovich), the resistive sheet, and its dual, the magnetically conducting sheet boundary. The integral equation formulations presented for a general geometry are specialized for bodies of revolution and solved with the method of moments (MM). The current expansion functions, which are chosen, result in a symmetric system of equations. This system is expressed in terms of two Galerkin matrix operators that have special properties. The solutions of the integral equation for the impedance boundary at internal resonances of the associated perfectly conducting scatterer are examined. The results are compared with the Mie solution for impedance-coated spheres and with the MM solutions of the electric, magnetic, and combined field formulations for impedance-coated bodies.     

Electromagnetic Scattering From Arbitrarily Shaped Dielectric Bodies Using Paired Pulse Vector Basis Functions and Method of Moments

A pair of orthogonal pulse vector basis functions is demonstrated for the calculation of electromagnetic scattering from arbitrarily-shaped material bodies. The basis functions are intended for use with triangular surface patch modeling applied to a method of moments (MoM) solution. For modeling the behavior of dielectric materials, several authors have used the same set of basis functions to represent equivalent electric and magnetic surface currents. This practice can result in zero-valued or very small diagonal terms in the moment matrix and an unstable numerical solution. To provide a more stable solution, we have developed orthogonally placed, pulse basis vectors: one for the electric surface current and one for the magnetic surface current. This combination ensures strongly diagonal moment matrices. The basis functions are suitable for electric field integral equation (EFIE), magnetic field integral equation (HFIE), and combined field formulations. In this work, we describe the implementations for EFIE and HFIE formulations and show example results for canonical figures.      

Scattering from multiple conducting and dielectric bodies ofarbitrary shape

A simple moment-method solution is presented for the problem of electromagnetic scattering from structures consisting of multiple perfectly conducting and dielectric bodies of arbitrary shape. The system is excited by a plane wave. The surface equivalence principle is used to replace the bodies by equivalent electric and magnetic surface currents, radiating into an unbounded medium. A set of coupled integral equations, involving the surface currents, is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the bodies are approximated by planar triangular patches, and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. Results for the scattering cross sections are presented. The computed results are in very good agreement with the exact solutions and with published data     

Scattering by an infinite wedge with tensor impedance boundaryconditions-a moment method/physical optics solution for thecurrents

Plane wave scattering by an infinite, two-dimensional wedge whose faces are characterized by impedance tensors is discussed. A combination of the moment method (MM) and physical optics (PO) is used to obtain a solution for the equivalent electric currents. The currents near the edge on each face are expanded with a set of basis functions consisting of pulse functions, defined on a meshed region, plus a function spanning the whole face. The currents outside the meshed region are taken to be the sum of physical optics currents, taken to be known, plus the whole-face basis function current. Expressing the equivalent magnetic currents in terms of the electric currents through the impedance tensors, the expansion coefficients for the electric current expansion are determined through an MM solution of the magnetic field integral equation. Sample results for wedges with isotropic and anisotropic face impedances are presented     

Using half-plane solutions in the context of MM for analyzing largeflat structures with or without resistive loadings

The size of the scatterers that can be analyzed using the conventional method of moments (MM) is limited to only a few wavelengths, due to large storage requirements in the computer. One way to circumvent this problem is to use techniques that temper the growth in the size of the impedance matrix to a reasonable level even as the scatterer becomes large in terms of the wavelength. It is shown that this can be done by choosing an appropriate set of entire or semi-entire domain basis functions that incorporate the actual physics of the scattering phenomenon. The functional forms of the basis functions are obtained either from an exact or an asymptotic solution to certain canonical problems. As an example, the problems of scattering from perfectly conducting or resistively loaded flat strips and plates are solved by utilizing the exact or asymptotic solutions to half-plane problems as basis functions     

An asymptotic high-frequency analysis of the radiation by a sourceon a perfectly conducting convex cylinder with an impedance surfacepatch [antennas]

A high-frequency approximation is presented for the fields radiated by a magnetic line or line dipole source which is located on an impedance surface patch that partly covers an electrically large, perfectly conducting convex cylinder. Relatively simple asymptotic approximations are developed for the currents induced on the impedance surface by the line sources, and the radiation patterns are calculated by incorporating these surface currents into the radiation integral. The latter integral exists only over the patch region as it uses a perfectly conducting cylinder Green's function which is expressed in terms of a uniform geometrical diffraction (UTD) solution. Numerical results are presented and shown to compare very well with other independent calculations and measurements     

Electromagnetic scattering by a perfectly conducting patch array ona dielectric slab

The scattering characterization of an infinite and truncated periodic array of perfectly conducting patches on a dielectric slab is discussed. In particular, an approximate solution for the truncated array scattering that is based on the exact solution for the corresponding infinite array is presented. The latter is obtained numerically by solving for the patch currents using a conjugate-gradient fast Fourier transform (FFT) technique, eliminating the need to generate and store the usual square impedance matrix. The scattering pattern of the finite array is then computed approximately by integrating the infinite-period-array currents over the given finite array. Numerical results are presented for the infinite and finite arrays, and the accuracy of the approximate solution for the finite array is examined and discussed in relation to some available exact data. It is found that the approximate solution is of reasonable accuracy in predicting the scattering by the truncated array     

Study of mixed-order basis functions for the locally corrected Nystro/spl uml/m method

A high-order locally corrected Nystro/spl uml/m (LCN) method employing the mixed-order basis functions proposed by C$80al/spl iota/s$80kan and Peterson is presented for the electromagnetic scattering by targets composed of both dielectric and conducting bodies. An integral operator based on a combined field formulation for conducting surfaces and a Mu/spl uml/ller formulation for dielectric surfaces is used. It is found that for general scattering objects, mixed-order basis functions accelerate the convergence of the LCN solution, can eliminate spurious charges, and can significantly reduce the condition number of the impedance matrix.     

TM and TE scattering by a dielectric/ferrite cylinder in the presence of a half-plane

An integral equation solution to the problem of transverse magnetic (TM) or transverse electric (TE) scattering by an isotropic dielectric/ferrite material cylinder in the presence of a perfectly conducting half-plane is presented. The technique is termed a method of moments (MM)/Green's function solution since the method of moments is used to determine the electric and magnetic polarization currents representing the material cylinder, while the presence of the half-plane is accounted for by including the half-plane Green's function in the kernel of the integral equations. Numerical results are presented for the echo width, material cylinder interior fields, and the surface impedance of a material slab on the surface of a half-plane.     

Electromagnetic scattering from electrically large coated flat and curved strips: Entire domain Galerkin formulation

Efficient numerical solutions are presented for electromagnetic scattering for classes of electrically large, coated, perfectly conducting strips which are flat or curved. The formulation is based on the solution of a coupled system of electric- and magnetic-field integral equations using the method of moments (MM). Entire domain Galerkin representations for the currents are used on the surface of the coating and at the coating-conductor interface. The resulting symmetric matrix equation is well conditioned and admits rapid, accurate solutions. Numerical results are presented for various coating thicknesses, strip widths, and curvatures for the transverse electric (TE) and transverse magnetic (TM) cases. The convergence of the Galerkin solution is examined as a function of these parameters. The effect of the edge approximation on the choice of expansion functions is discussed. The numerical results are compared with experimental measurements.     

A hybrid moment method solution for TEz scattering fromlarge planar slot arrays

This paper develops a hybrid moment method (MM) based numerical model for electromagnetic scattering from large finite-by-infinite planar slot arrays. The model incorporates the novel concept of a physical basis function (PBF) to reduce dramatically the number of required unknowns. The model can represent a finite number of slot columns with slots oriented along the infinite axis, surrounded by an arbitrary number of coplanar dielectric slabs. Each slot column can be loaded with a complex impedance to tailor the array's edge currents. An individual slot column is represented by equivalent magnetic scattering currents on an unbroken perfectly conducting plane. Floquet theory reduces the currents to a single reference element. In the array's central portion, where the edge perturbations are negligible, the slot column reference elements are combined into a single basis function. Thus, one PBF can represent an arbitrarily large number of slot columns. A newly developed one-sided Poisson sum formula is used to calculate the mutual coupling between the PBF and the slot columns in the presence of a stratified dielectric media. The array scanning method (ASM) gives the mutual coupling between the individual slot columns. The hybrid method is validated using both numerical and experimental reference data. The results demonstrate the method's accuracy as well as its ability to handle array problems too large for traditional MM solutions     

Generalized network parameters, radiation and scattering by conducting bodies of revolution

Introduces computer programs (FORTRAN IV) designed for field calculation from conducting bodies of revolution. A set of four programs which calculate the generalised impedance matrix and admittance matrix for triangular expansion functions, bistatic radar scattering for an axially incident plane wave, radiation from rotationally symmetric aperture antennas, and radar backscattering for an obliquely incident plane wave, are presented. Results for a number of examples are summarised and discussed. The accuracy of computation depends on the smoothness of the body and of the excitation     

Application of adaptive basis functions for a diagonal moment matrix solution of arbitrarily shaped three-dimensional conducting body problems

We present the application of specially constructed adaptive basis functions that generate a diagonal matrix in the method of moments solution procedure for the calculation of scattered electromagnetic fields from arbitrarily shaped conducting bodies excited by a plane electromagnetic wave. The arbitrary body is modeled using planar triangular patches. The crucial step in the solution procedure is the construction of the adaptive basis functions to generate the diagonal matrix. This task is accomplished with the help of well-known RWG basis functions. The solution thus obtained is very efficient, accurate, and applicable to truly arbitrary bodies. Several numerical examples are presented to validate the new method.     

Electromagnetic radiation and scattering from finite conducting anddielectric structures: surface/surface formulation

An efficient and accurate numerical procedure for the analysis of the electromagnetic scattering and radiation from arbitrarily shaped, composite finite conducting and dielectric bodies is proposed. A set of coupled electric field integral equations involving surface equivalent electric and magnetic currents is used. The coupled integral equations are solved through planar triangular patch modeling and the method of moments. Two separate, mutually orthogonal vector functions for each edge connecting a pair of triangular patches have been developed. Numerical results for disk/cone and cylinder/cone structures are compared with other available data. Limited comparison with experimental data has also been made     

二维多导体柱电磁散射特性的特征基函数法分析

特征基函数法是近两年提出来的一种求解电磁散射问题的有效方法,该方法使用的特征基函数不受传统矩量法离散尺寸的限制,因而可以大大减小要求解的矩阵方程。应用特征基函数法分析了二维多导体柱的电磁散射特性,计算了多个无限长导电椭圆柱和方柱的雷达散射截面,结果表明特征基函数法的计算结果与传统矩量法的计算结果吻合良好,而计算量却大为减少。     

Numerical solution of time domain integral equations for arbitrarily shaped conductor/dielectric composite bodies

In this work, we present a numerical solution of the coupled time domain integral equations to obtain induced currents and scattered far fields on a three-dimensional, arbitrary shaped conducting/dielectric composite body illuminated by a Gaussian electromagnetic plane wave pulse. The coupled integral equations are derived utilizing the equivalence principle. The solution method is based on the method of moments and involves the triangular patch modeling of the composite body, in conjunction with the patch basis functions. Detailed mathematical steps along with several numerical results are presented to illustrate the efficacy of this approach.     

A moment method approach using frequency-independent parametricmeshes

A moment method (MM) formulation using nonuniform rational B-splines (NURBS) parametric surfaces is introduced to analyze radiation and scattering from arbitrarily shaped conducting bodies. A feature of the technique presented is the independence of the geometrical model from the frequency which avoids the regeneration of the geometry model when the frequency changes. This feature is obtained by defining new sets of basis and testing functions that extend over subpatches in each NURBS. The proposed approach is accurate, flexible, and efficient