Scattering from planar structures containing small features usingthe adaptive integral method (AIM)

Fast integral equation algorithms such as the adaptive integral method (AIM) have been demonstrated to reduce memory and execution time associated with moment-method solutions for arbitrarily shaped three-dimensional (3-D) geometries. In this paper, we examine the efficiency of AIM in modeling planar structures that contain small and intricate details as is the case with spirals and slot antennas. Such geometries require high tessellation due to the inclusion of very small features resulting in a large number of unknowns. AIM with its capability to translate the original grid to an equivalent sparser uniform grid is uniquely suited for the analysis of such geometries. In the latter part of the paper, we demonstrate the application of AIM in connection with a finite-element boundary-integral formulation for cavity-backed antennas     

A thin-rod approximation for the improved modeling of bare and insulated cylindrical antennas using the FDTD method

A general and consistent integral finite-difference time-domain (FDTD) formulation on cubical grids for modeling of cylindrical antennas with or without dielectric coating is derived. No additional grid points or modifications of the integral paths are necessary. Instead, effective material properties are modified in the FDTD grid. Thus, even for insulated antennas, the simple cubical structure is maintained. Special integral factors are defined on cubical elements, which take into account the behavior of fields in all directions in the neighborhood of the antenna. Applying these factors to the gap region and along the antenna's axis allows a correct modeling of the influence of the antenna's thickness. Furthermore, integral factors derived for the antenna's ends improve the modeling of the antenna's length. The accuracy of the method is confirmed by a systematic comparison with analytical and numerical results.     

Loop-tree implementation of the adaptive integral method (AIM) for numerically-stable, broadband, fast electromagnetic modeling

The adaptive integral method (AIM) is implemented in conjunction with the loop-tree (LT) decomposition of the electric current density in the method of moments approximation of the electric field integral equation. The representation of the unknown currents in terms of its solenoidal and irrotational components allows for accurate, broadband electromagnetic (EM) simulation without low-frequency numerical instability problems, while scaling of computational complexity and memory storage with the size of the problem are of the same order as in the conventional AIM algorithm. The proposed algorithm is built as an extension to the conventional AIM formulation that utilizes roof-top expansion functions, thus providing direct and easy way for the development of the new stable formulation when the roof-top based AIM is available. A new preconditioning strategy utilizing near interactions in the system which are typically available in the implementation of fast solvers is proposed and tested. The discussed preconditioner can be used with both roof-top and LT formulations of AIM and other fast algorithms. The resulting AIM implementation is validated through its application to the broadband, EM analysis of large microstrip antennas and planar interconnect structures.     

Adaptive Nonuniform-Grid (NG) Algorithm for Fast Capacitance Extraction

A novel method for computing the capacitance matrices of arbitrary shaped three-dimensional geometries is presented. The proposed approach combines a novel nonuniform-grid (NG) algorithm for fast evaluation of potentials due to given source distributions with an iterative solution of the pertinent integral equations. The NG algorithm is based on the observation that locally the potential produced by a finite size source can be interpolated from its samples at a small number of points of a nonuniform spherical grid. This observation leads to a multilevel algorithm comprising interpolation and aggregation of potentials. The resulting hierarchical algorithm attains an$O (N)$asymptotic complexity and memory requirements. The computational efficiency is further improved for quasi-planar geometries by the use of adaptive grids.     

Experimental design of a two-layer electromagnetically coupledrectangular patch with a global response surface modeling technique

A new approach, based on global response surface (GRS) modeling techniques, is used to design two-layer electromagnetically coupled rectangular patch antennas. Data from a grid of design points is used to construct a model of the input impedance of the antenna. The model is then optimized to provide the best design geometries for the frequency band of interest. Three examples are presented to validate the method     

大尺寸天线的FDTD仿真

在三维Yee网格模型以及蛙跳模型基础上,分析了使用FDTD方法对天线的计算,重点讨论了非均匀网格技术和近远场转换原理,同时还研究了激励源以及吸收边界条件的具体实现办法。最后,以大尺寸喇叭天线为例,用理论和实验结果验证了计算方法的正确性,解决了大尺寸天线的FDTD仿真问题。     

Numerical calculations of the potential due to an arbitrary charge density using the fast Fourier transform

The Green's function method of finding the voltage due to an arbitrary charge density is related to a convolution integral for simple geometries. The fast Fourier transform (FFT) algorithm is used to calculate the voltages on the grid points and it is argued that significant reduction of computer time is achieved for a large number of grid points.     

Moment method analysis of infinite stripline-fed tapered slotantenna arrays with a ground plane

A full-wave method of moments solution for infinite arrays of stripline-fed tapered slot antennas is described. The formulation of the problem is sufficiently general to permit performance evaluation of most of the geometries that have been proposed for stripline-fed antennas as well as of several other types of array antennas. Computed results for some well-known antenna arrays are presented to demonstrate the validity and accuracy of the method. Excellent agreement with published results has been obtained for scattering from corrugated surfaces and grounded dielectric slabs and for the input impedance of dipole and monopole arrays. Catastrophic effects such as scan blindness are accurately predicted. A sample result showing the measured and computed input impedance of a stripline-fed tapered slot antenna array is also presented     

The Analysis of Monopole Antennas Located on a Spherical Vehicle: Part 2, Numerical and Experimental Results

Presented are various numerical results illustrating the behavior of thin monopole antennas located on a perfectly conducting sphere. The method of analysis, described in a previous paper, uses an integral equation solution for the unknown wire currents, and a modified Green's function to limit the range of integration to over the wires only. Studies are made of the input quantities, radiated currents and induced sphere currents for various antenna geometries. A comparison of the computed input impedance of monopole on the sphere is made with experimental data and good agreement is noted.     

A hybrid finite element-boundary integral method for the analysisof cavity-backed antennas of arbitrary shape

An edge-based hybrid finite element-boundary integral (FE-BI) formulation using tetrahedral elements is described for scattering and radiation analysis of arbitrarily shaped cavity-backed patch antennas. By virtue of the finite element method (FEM), the cavity irregularities, the dielectric super/substrate inhomogeneities, and the diverse excitation schemes inside the cavity may be readily modeled when tetrahedral elements are used to discretize the cavity. On the aperture, the volume mesh reduces to a triangular grid allowing the modeling of nonrectangular patches. Without special handling of the boundary integral system, this formulation is typically applicable to cavity-backed antenna systems with moderate aperture size. To retain an O(N) memory requirement, storage of the full matrix due to the boundary integral equation is avoided by resorting to a structured triangular aperture grid and taking advantage of the integral's convolutional property. If necessary, this is achieved by overlaying a structured triangular grid on the unstructured triangular grid and relating the edge field coefficients between the two grids via two narrow banded transformation matrices. The combined linear system of equations is solved via the biconjugate gradient (BICG) method, and the FFT algorithm is incorporated to compute the matrix-vector product efficiently, with minimal storage requirements     

A separation of the logarithmic singularity in the exact kernel of the cylindrical antenna integral equation

The well-known logarithmic behavior of the singular "exact" kernel of cylindrical antenna integral equations is explicitly separated. The elliptic integral partitioning of the kernel by Schelkunoff is the point of departure in the development. The result is an expression for the kernel comprising the logarithmic term and a well-behaved economically computable residual term. This result is readily amenable to numerical solutions of integral equations of cylindrical geometries. Numerical results obtained from method-of-moments solutions to cylindrical antennas are given to verify the result.     

Electromagnetic modeling of passive circuit elements in MMIC

A spatial domain mixed-potential integral equation method is developed for the analysis of microstrip discontinuities and antennas of arbitrary shape. The algorithm is based on roof-top basis functions on a rectangular and triangular mixed grid and analytical evaluation of the quadruple moment integrals involved. The algorithm has been successfully implemented into an accurate, efficient, and versatile computer program. The numerical results agree with the measured ones very well     

Optimized basis functions for slot antennas excited by coplanar waveguides

A method is proposed for the analysis of slot antennas excited by coplanar waveguides. First, a standard integral equation for the continuity of the magnetic field is formulated. Then the appropriate equivalent magnetic currents of the method of moments are represented in terms of entire-domain basis functions which synthesize the resonant behavior of the slot and the field in proximity of the feeding source and of the bends. In order to define these basis functions, canonical geometries are identified, whose Green's functions have been found analytically. The accuracy and the effectiveness of the method in terms of convergence rate and number of unknowns is demonstrated by comparison with a standard fine meshing full-wave analysis.     

The time domain integral equation for a straight thin-wire antenna with the reduced kernel is not well-posed

We show that the Pocklington integral equation for time-domain scattering from thin-wire antennas is not mathematically well-posed. This has considerable implications for numerical solution schemes. In particular, our argument explains the observed occurrence of rapidly oscillating errors in numerical solutions as the numerical grid sizes are reduced.     

A fast sinc function gridding algorithm for fourier inversion in computer tomography

The Fourier inversion method for reconstruction of images in computerized tomography has not been widely used owing to the perceived difficulty of interpolating from polar or other measurement grids to the Cartesian grid required for fast numerical Fourier inversion. Although the Fourier inversion method is recognized as being computationally faster than the back-projection method for parallel ray projection data, the artifacts resulting from inaccurate interpolation have generally limited application of the method. This paper presents a computationally efficient gridding algorithm which can be used with direct Fourier transformation to achieve arbitrarily small artifact levels. The method has potential for application to other measurement geometries such as fan-beam projections and diffraction tomography and NMR imaging.     

Analysis of arbitrarily shaped dielectric radomes using adaptive integral method based on volume integral equation

The adaptive integral method (AIM) is employed to solve the volume integral equation (VIE) for analyzing the radiation of the antenna with an arbitrarily shaped radome. Small dipoles are used as exciting sources. Modeling the radomes by tetrahedron cells, the induced volume current is determined by the AIM based on VIE. The application of AIM significantly reduces CPU time and computer memory requirement. Hence, the method presented in the paper can be applied to simulate electrically large sized radomes. Finally, the radiation patterns of small dipole arrays in the presence of spherical and conical radomes are calculated.     

A uniformly valid loaded antenna theory

A quasi-static layered approximation is used to simplify the layered solution for insulated antennas to the solution of a generalized impedance boundary value problem, whose solution is expressed in terms of an integral. This integral applies to insulated antennas imbedded in a dense medium, insulated antennas imbedded in air (dielectric-coated antennas), and impedance-loaded antennas, all referred to as loaded antennas. The branch cut contribution for large distances is given by the Sommerfeld space wave formula. The physical transition of loaded antennas to bare antennas is investigated through the asymptotic evaluation of this integral. Simple uniform formulas for loaded antenna current are derived and generalized to cover the same range of validity as the integral. The direct calculation of the input admittance is consistent with the derived uniform formula for antenna current. For insulated antennas in a dense medium, the complete transmission line theory describes the antenna current through the transition to bare antennas     

A comparison between two kinds of equivalent currents to analyze conducting bodies with apertures using moment methods: Application to horns with symmetry of revolution

A system of integral equations (SIE) based on the unique-hess theorem that uses only electric equivalent currents (EEC) is formulated to analyze conducting bodies with apertures. This SIE is compared with an SIE that uses both electric and magnetic equivalent currents (EMEC). In general, to solve both SIE's numerically difficult computations of Cauchy principal-value integrals with highly singular kernels are required. These integrals appear when computing electric (magnetic) fields created by magnetic (electric) currents. Their evaluation can be avoided using the EEC approach in many practical cases when the main interest is in the radiation patterns of aperture antennas. The two SIE's are compared by carrying out an analysis of rotationally symmetric horns using the moment method (MM) in its formulation for bodies of revolution. Numerical results of electric currents and radiation patterns are presented for small horns of various geometries. These results compare quite well with measurements for both SIE's. However, the central processing unit (CPU) time for the EEC formulation is an order of magnitude smaller than for the EMEC formulation.     

积分方程的多重网格解法及其在天线分析中的应用

本文将多重网格方法应用于积分方程，建立了Ｆｒｅｄｈｏｌｍ积分方程的多重网格解法，并将其应用于线天线的分析研究，对不同长度的线天线进行了数值分析，得到了较好的结果。数值实验表明，多重网格方法是一种十分有效的快速迭代方法，为分析大阵问题提供了一种新的数值方法