A combined full-wave CG-FFT method for rigorous analysis of largemicrostrip antenna arrays

An accurate and efficient technique is presented for the analysis of large microstrip antenna arrays. The technique consists of an amalgamation of a spatially discrete scheme, consisting of the CG-FFT method and the complex discrete image (CDI) technique. The unique feature of this approach is the use of the spatially discrete CG-FFT for analyzing microstrip structures. The aliasing and truncation errors are thoroughly eliminated in this approach. In addition, the grad-div operators are transformed from singular Green's functions to differentiable expansion and testing functions by using Galerkin's procedure, thereby improving the accuracy and the rate of convergence. To show the accuracy and efficiency of this technique, a number of microstrip arrays, including a large microstrip reflectarray, have been studied. It is found that the simulations carried out using this technique are in very good agreement with measurements     

Spectral domain analysis of conducting patches of arbitrarygeometry in multilayer media using the CG-FFT method

A conjugate gradient-fast Fourier transform (CG-FFT) scheme for analyzing finite, flat, metallic patches in multilayer structures is presented. Rooftop and razor-blade functions are considered as basis and testing functions, respectively. An equivalent periodic problem in both domains (real and spectral) is obtained and solved. Aliasing problems are avoided by performing a window on the Green's function. The spectral domain periodicity makes it feasible to take into account almost all the harmonics and to reduce the ripple in the computed current distributions. Nearly all the operations are performed in the spectral domain, including Green's function computations. Several results of convergence rates, current distributions and radar cross-section (RCS) values are given and compare favorably with measurements or results obtained by other methods     

A numerical scheme to obtain the RCS of three-dimensional bodies ofresonant size using the conjugate gradient method and the fast Fouriertransform

A numerical scheme to obtain radar cross section (RCS) of three-dimensional bodies of resonant size (BRS) with arbitrary geometry and material composition is described. The RCS is obtained by solving the electric-field integral equation (EFIE) using the conjugate gradient-fast Fourier transform method (CG-FFT). The choice of a suitable set of basis and testing functions to discretize the EFIE leads to a very accurate and computationaly efficient CG-FFT procedure. This accuracy is checked by comparison with RCS measurements or predictions by other methods. As compared to the moment method, this CG-FFT scheme avoids the storage of large matrices and reduces the computer time by orders of magnitude     

An improved pulse-basis conjugate gradient FFT method for the thinconducting plate problem

A conjugate-gradient fast Fourier transform (CG-FFT) formulation for the scattering by a thin, perfectly conducting plate is presented. Pulse basis functions and a Dirac δ function are used for expansion and testing purposes, respectively. Particular attention is paid to the generation of the terms in the impedance matrix of the resulting matrix equation. Except for the self-coupling terms, all the other terms are computed by explicit integrations. Comparison with two previously reported pulse-basis CG-FFT formulations shows that the present method is more stable when the error tolerance of the solution is reduced. When sufficient cell discretizations are used, smooth distributions can be obtained which resemble those obtained via rooftop-CG-FFT formulation. The numerical results are further validated by comparing the far-field radar cross section with an analytical technique for a circular plate     

Detection of buried targets using a new enhanced very early timeelectromagnetic (VETEM) prototype system

In this paper, numerical simulations of a new enhanced very early time electromagnetic (VETEM) prototype system are presented, where a horizontal transmitting loop and two horizontal receiving loops are used to detect buried targets, in which three loops share the same axis and the transmitter is located at the center of receivers. In the new VETEM system, the difference of signals from two receivers is taken to eliminate strong direct-signals from the transmitter and background clutter and furthermore to obtain a better SNR for buried targets. Because strong coupling exists between the transmitter and receivers, accurate analysis of the three-loop antenna system is required, for which a loop-tree basis function method has been utilized to overcome the low-frequency breakdown problem. In the analysis of scattering problem from buried targets, a conjugate gradient (CG) method with fast Fourier transform (FFT) is applied to solve the electric field integral equation. However, the convergence of such CG-FFT algorithm is extremely slow at very low frequencies. In order to increase the convergence rate, a frequency-hopping approach has been used. Finally, the primary, coupling, reflected, and scattered magnetic fields are evaluated at receiving loops to calculate the output electric current. Numerous simulation results are given to interpret the new VETEM system. Comparing with other single-transmitter-receiver systems, the new VETEM has better SNR and ability to reduce the clutter     

Efficiently convergent novel basis functions for the analysis of microstrip discontinuities by the spectral domain Galerkin method

In this paper, novel efficient basis functions are presented for the rigorous analysis by the spectral domain Galerkin method of geometrically complex Microstrip discontinuities. The numerical performances of these basis functions are very attractive, namely, very rapid convergence and high stability. Moreover, a comparative study of the convergence features of the proposed basis functions with two others widely used in literature, namely, the rooftops and the rectangular pulses, is presented. To illustrate this study, numerical results are presented for a shielded Microstrip bend discontinuity.     

Analysis of arbitrary metallic surfaces conformed to a circularcylinder using the conjugate gradient-fast Fourier transform (CG-FFT)method

An efficient scheme for analyzing electrodynamic problems involving arbitrary metallic surfaces conformed to a circular cylinder, using the conjugate-gradient-fast-Fourier-transform (CG-FFT) method, is presented. The numerical method outlined is efficient in CPU time and minimizes the memory storage requirements. Several results are presented and compared with numerical or measured values that appear in the literature     

The hybrid extended Born approximation and CG-FFT method forelectromagnetic induction problems

The authors propose the hybridization of the extended Born approximation (EBA) with the conjugate-gradient fast Fourier transform (CG-FFT) method to improve the efficiency of numerical solution of electromagnetic induction problems. This combination improves the solution efficiency in two ways. First, using the FFT in the extended Born approximation decreases the computational cost of the conventional EBA method from O(N²) to O(N log₂ N) arithmetic operations, where N is the number of unknowns in the problem. This approach, referred to as the FFT-EBA method, applies to problems with a fairly large contrast. Secondly, using the EBA as a partial preconditioner for the CG-FFT method increases the convergence speed of the conventional CG-FFT method. This second approach, referred to as the EBA-CGFFT method, is in principle applicable to all problems with a homogeneous background, but is particularly efficient for problems with a higher contrast. Numerical experiments suggest that the combination of these two methods is more accurate and more efficient for electromagnetic induction problems     

多层各向异性等离子体球电磁散射的解析解

给出s层各向异性等离子体球电磁场球矢量波函数解析表达式,应用电磁场在(s-1)层球壳边界上切向电磁场连续以及辐射条件,导出了平面波入射情况下,s层等离子体球电磁场的展开系数。将数值计算结果分别与矩量法-共扼梯度-傅里叶变换(MOM-CG-FFT)计算结果和均匀等离子体球的结果进行了比较,符合得较好。该文研究结果预期可应用于新型天线的研制和卫星通信等领域。     

A combined finite element-boundary integral formulation forsolution of two-dimensional scattering problems via CGFFT

A novel technique is presented for computing the scattering by two-dimensional structures of arbitrary inhomogeneity. The proposed approach combines the usual finite-element (FE) method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are then convolutions and can be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach presented here offers the principal advantage of having O(N) memory demand and employs a one-dimensional FFT, as against the two-dimensional FFT required in a traditional implementation of the proposed CG-FFT algorithm. The speed of the proposed solution method is compared with that of the traditional CG-FFT algorithm. Results are presented for several rectangular composite cylinders and one perfectly conducting cylinder. These are shown to be in excellent agreement with the moment method     

Limitations of the Cubical Block Model of Man in Calculating SAR Distributions

Block models of man which consist of a limited number of cubical cells are commonly used to predict the internal electromagnetic (EM) fields and specific absorption rate (SAR) distributions inside the human body. Numerical results, for these models, are obtained based on moment-method solutions of the electric-field integral equation (EFIE) with a pulse function being used as the basis for expanding the unknown internal field. In this paper, we first examine the adequacy of the moment-method procedure, with pulse basis functions, to determine SAR distributions in homogeneous models. Calculated results for the SAR distributions in some block models are presented, and the stability of the solutions is discussed. It is shown that, while the moment-method, using pulse basis functions, gives good values for whole-body average SAR, the convergence of the solutions for SAR distributions is questionable. A new technique for improving the spatial resolution of SAR distribution calculations using a different EFIE and Galerkin's method with linear basis functions and polyhedral mathematical cells is also described.     

Hierarchal vector basis functions of arbitrary order for triangularand tetrahedral finite elements

New vector finite elements are proposed for electromagnetics. The new elements are triangular or tetrahedral edge elements (tangential vector elements) of arbitrary polynomial order. They are hierarchal, so that different orders can be used together in the same mesh and p-adaption is possible. They provide separate representation of the gradient and rotational parts of the vector field. Explicit formulas are presented for generating the basis functions to arbitrary order. The basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning. Matrix assembly for the frequency-domain curl-curl equation is conveniently carried out by means of universal matrices. Application of the new elements to the solution of a parallel-plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient, for tetrahedral elements to order 4. In particular, the full-order elements have only the same asymptotic convergence rate as elements with a reduced gradient space (such as the Whitney element). However, further tests reveal that the optimum balance of the gradient and rotational components is problem-dependent     

A Novel Efficient Technique for the Calculation of the Green's Functions in Rectangular Waveguides Based on Accelerated Series Decomposition

A new efficient technique for computing the Green's functions inside rectangular waveguides is presented. After a summary of the classical approaches and their difficulties, a new strategy is proposed, based on the decomposition of the main spectral series into simpler terms. Although the resulting series present better convergence rate, several acceleration techniques are combined to further improve the efficiency. Several results are presented to demonstrate the improvements in convergence rates obtained using the new decomposition.     

A New Class of Basis Functions for the Solution of the E-Plane Waveguide Discontinuity Problem

A class of basis functions which satisfies the edge condition explicitly is presented to improve the convergence of the mode-matching method. Using these basis functions, we analyse the 2-to-1 E-plane junction, make comparisons with other available methods of solution, and provide correction terms for its quasi-static solution.     

2-D validation of a formulation for the analysis of 3-D bodies thatare periodic in one direction and finite sized in the others

A numerical scheme to analyze three-dimensional bodies that are periodic in one direction (z) and finite sized in the other ones (x, y) is presented. The geometry and material composition of the body can be arbitrary. A new formulation using the conjugate gradient-fast Fourier transform method (CG-FFT) has been developed. The formulation is based on the discretization and resolution of the electric field integral equation (EFIE) in both the real and spectral domains and leads to an efficient and accurate numerical procedure. Results are presented for RCS, equivalent currents and fields inside 3-D periodic structures (infinitely long cylinders with arbitrary shape and material composition). These results are compared with analytical solutions and the agreement is found to be good     

Iterative algorithm for nonuniform inverse fast Fourier transform(NU-IFFT)

A nonuniform inverse fast Fourier transform (NU-IFFT) for nonuniformly sampled data is realised by combining the conjugate-gradient fast Fourier transform (CG-FFT) method with the newly developed nonuniform fast Fourier transform (NUFFT) algorithms. An example application of the algorithm in computational electromagnetics is presented     

Quasi-optical grids with thin rectangular patch/aperture elements

Theoretical analysis is presented for an efficient and accurate performance evaluation of quasi-optical grids comprised of thin rectangular patch/aperture elements with/without a dielectric substrate/superstrate. The convergence rate of this efficient technique is improved by an order of magnitude with the approximate edge conditions incorporated in the basis functions of the integral equation solution. Also presented are the interesting applications of this efficient analytical technique to the design and performance evaluation of the coupling grids and beam splitters in the optical systems as well as thermal protection sunshields used in the communication systems of satellites and spacecrafts.     

Comparison between two sets of basis functions for the currentmodeling in the Galerkin spectral domain solution for microstrips

A frequently used technique for the numerical full wave analysis of planar microwave passive structures is the method of moments (MoM). A very important determinant for the accuracy and efficiency of this technique is the choice of the basis functions used in the approximation of the unknown current components. The application of several types of entire and subsectional domain basis functions has been proposed in the literature. However, little comparison has been made between different types of basis functions. In this paper, a comparison is presented between two sets of frequently used subsectional domain basis functions for the canonical case of the microstrip transmission line. The emphasis in this paper is on the relative accuracy, the convergence and the computational efficiency of both sets of basis functions. The intent of the paper is primarily to be an eye opener for the implications of the choice of the basis functions     

Eigenvalues of the moment-method matrix and their effect on theconvergence of the conjugate gradient algorithm [EM scattering]

A theory that relates eigenvalues of a continuous operator to those of the moment-method matrix operator is discussed and confirmed by examples. This theory suggests reasons for ill conditioning when certain types of basis and testing functions are used. In addition, the effect of eigenvalue location on the convergence of the conjugate gradient (CG) method is studied. The convergence rate of the CG method is dependent on the eigenvalues of the iteration matrix as well as on the number of eigenvectors of the iteration matrix needed to represent the right side of the equation. These findings explain the previously reported convergence behavior of the CG method when applied to electromagnetic-scattering problems     

Efficient electromagnetic modeling of three-dimensional multilayermicrostrip antennas and circuits

An efficient method-of-moments (MoM) solution is presented for analysis of multilayer microstrip antennas and circuits. The required multilayer Green's functions are evaluated by the discrete complex image method (DCIM), with the guided-mode contribution extracted recursively using a multilevel contour integral in the complex _ρ-plane. An interpolation scheme is employed to further reduce the computer time for calculating the Green's functions in the three-dimensional (3-D) space. Higher order interpolatory basis functions defined on curvilinear triangular patches are used to provide necessary flexibility and accuracy for the discretization of arbitrary shapes and to offer a better convergence than lower order basis functions. The combination of the improved DCIM and the higher order basis functions results in an efficient and accurate MoM analysis for 3-D multilayer microstrip structures