Some scattering results computed by surface-integral-equation and hybrid finite-element - boundary-integral techniques, accelerated by the multilevel fast multipole method

Method-of-moments (MoM) solutions of surface integral equations are especially well suited for scattering computations involving metallic objects. Improved modeling flexibility for dielectric (possibly lossy) and mixed dielectric/metallic bodies is obtained by combining a surface-integral-equation formulation, involving electric and magnetic equivalent surface-current densities, with a volumetric finite-element (FE) model of the dielectric regions. This results in the well-known hybrid FEBI (finite-element-boundary-integral) technique. For many years, hybrid FEBI techniques, as well as stand-alone Bl (surface-integral equation, often just termed MoM) techniques, were restricted to relatively small (with respect to a wavelength) geometries. However, with the development of powerful multilevel fast multipole methods/algorithms (MLFMM/MLFMA), it has become possible to compute a larger variety of practical scattering and radiation problems with the hybrid FEBI-MLFMM technique. In this contribution, we give a short review of our hybrid FEBI-MLFMM approach, with a focus on mixed dielectric/metallic geometries and multiple Bl domains. We then present a variety of scattering results for metallic and mixed dielectric/metallic objects, together with comparisons with measured RCS (radar cross section) data. Broadband computations are used to derive high-resolution range (HRR) profiles of several configurations.     

Human exposure assessment in the near field of GSM base-station antennas using a hybrid finite element/method of moments technique

A hybrid finite-element method (FEM)/method of moments (MoM) technique is employed for specific absorption rate (SAR) calculations in a human phantom in the near field of a typical group special mobile (GSM) base-station antenna. The MoM is used to model the metallic surfaces and wires of the base-station antenna, and the FEM is used to model the heterogeneous human phantom. The advantages of each of these frequency domain techniques are, thus, exploited, leading to a highly efficient and robust numerical method for addressing this type of bioelectromagnetic problem. The basic mathematical formulation of the hybrid technique is presented. This is followed by a discussion of important implementation details-in particular, the linear algebra routines for sparse, complex FEM matrices combined with dense MoM matrices. The implementation is validated by comparing results to MoM (surface equivalence principle implementation) and finite-difference time-domain (FDTD) solutions of human exposure problems. A comparison of the computational efficiency of the different techniques is presented. The FEM/MoM implementation is then used for whole-body and critical-organ SAR calculations in a phantom at different positions in the near field of a base-station antenna. This problem cannot, in general, be solved using the MoM or FDTD due to computational limitations. This paper shows that the specific hybrid FEM/MoM implementation is an efficient numerical tool for accurate assessment of human exposure in the near field of base-station antennas.     

Radiation and scattering from infinite periodic printed antennaswith inhomogeneous media

The hybrid method of moments (MoM)/Green's function method technique is applied to infinite periodic printed antenna arrays containing dielectric inhomogeneities. The solution uses an integral equation for an infinite periodic printed array on or over a homogeneous dielectric substrate, coupled with equivalent volume polarization currents for dielectric inhomogeneities on top of the homogeneous substrate. Volume pulse-basis functions were used to expand the volume polarization currents. A hybrid MoM/Green's function method solution was then obtained through the matrix form of the problem. The two-dimensional (2-D) solution of plane wave scattering from a grounded dielectric slab was used to validate the reaction impedance of the dielectric inhomogeneity. Several infinite periodic printed dipole arrays with dielectric supports and overlays were studied with this solution and good agreement was observed between the hybrid MoM/Green's function method and waveguide simulator experiments     

Higher order hybrid method of moments-physical optics modeling technique for radiation and scattering from large perfectly conducting surfaces

An efficient and accurate higher order, large-domain hybrid computational technique based on the method of moments (MoM) and physical optics (PO) is proposed for analysis of large antennas and scatterers composed of perfectly conducting surfaces of arbitrary shapes. The technique utilizes large generalized curvilinear quadrilaterals of arbitrary geometrical orders in both the MoM and PO regions. It employs higher order divergence-conforming hierarchical polynomial basis functions in the context of the Galerkin method in the MoM region and higher order divergence-conforming interpolatory Chebyshev-type polynomial basis functions in conjunction with a point-matching method in the PO region. The results obtained by the higher order MoM-PO are validated against the results of the full MoM analysis in three characteristic realistic examples. The truly higher order and large-domain nature of the technique in both MoM and PO regions enables a very substantial reduction in the number of unknowns and increase in accuracy and efficiency when compared to the low-order, small-domain MoM-PO solutions. The PO part of the proposed technique, on the other hand, allows for a dramatic reduction in the computation time and memory with respect to the pure MoM higher order technique, which greatly extends the practicality of the higher order MoM with a smooth transition between low- and high-frequency applications.     

A hybrid time-domain technique that combines the finite element, finite difference and method of moment techniques to solve complex electromagnetic problems

This paper describes a hybrid technique directly operating in time domain that combines the finite element time domain (FETD), the finite-difference time-domain (FDTD) and the integral-equation-based method of moments in the time domain (MoMTD) techniques to analyze complex electromagnetic problems involving thin-wire antennas radiating in the presence of inhomogeneous dielectric bodies whose shape can be arbitrary. The method brings together the ability of the FDTD scheme to deal with arbitrary material properties, the versatility of the FETD to accurately model curved geometries, and that of the MoM to analyze thin-wire structures. Working in the time domain provides wide-band information from a single execution of the marching-on-in-time procedure and simplifies the interfacing of the FE and MoM methods with the FDTD, an approach specifically designed for time domain analysis. Numerical results that validate the hybrid method and show its capabilities are presented in the paper.     

Study of the coupling between human head and cellular phone helical antennas

The interaction between normal-mode helical antennas and human head models is analyzed, using both a novel accurate semi-analytical method and finite-difference time-domain (FDTD) simulations. The semi-analytical method is based on the combination of Green's functions theory with the method of moments (Green/MoM) and is able to model arbitrarily shaped wire antennas radiating in the close proximity of layered lossy dielectric spheres representing simplified models of the human head. The purpose of the development of the Green/MoM technique is to provide a reliable tool for preliminary (worst case) estimation of human head exposure to the field generated by different antenna configurations with emphasis on the helical antenna, representing the most diffused antenna type used in modern cellular handsets. Furthermore, the accurate semi-analytical character of the Green/MoM technique permits the accuracy assessment of purely numerical techniques, such as the FDTD, which is currently the most widely used computational method in mobile communication dosimetric problems, since it allows modeling of anatomically based head models. After appropriate benchmarking, FDTD simulations are used to study the interaction between a heterogeneous anatomically correct model of the human head exposed to a normal-mode helix monopole operating at 1710 MHz mounted on the top of a metal box representing a realistic mobile communication terminal. The study of both canonical and realistic exposure problems includes computations of specific absorption rates (SARs) inside the human head, total power absorbed by the head and assessment of antenna performance. Emphasis is placed on the comparative dosimetric assessment between adults and children head models.     

Efficient modelling of finite-size ungrounded PCBs with a full wave3D moment-method analysis

A method in which 2D sheet-impedance elements are used to represent the finite-size dielectric substrate of an ungrounded PCB within a full wave 3D moment-method analysis (MoM) is presented. The use of these 2D elements significantly reduces both the core-memory demands and the CPU requirements of the MoM by an order of magnitude, with little compromise in accuracy     

金属介质混合目标电磁特性的快速分析

将自适应积分算法与基于体面混合积分方程的矩量法相结合快速分析任意结构金属/介质混合目标的电磁散射和辐射特性.通过将传统矩量法的阻抗矩阵分为两部分且采用不同的方法进行处理计算,提高了矩量法的计算速度并大幅度缩减了需要的计算机内存占用量.最后,分别用传统的矩量法与结合自适应积分快速算法的矩量法计算了三个典型例子,通过比较充分说明了文中方法的有效性.     

Hybrid technique combining finite element, finite difference andintegral equation methods in time domain

A new hybrid time domain method is presented which combines three well-known numerical techniques. i.e. the finite difference time domain (FDTD) method, finite element (FE) method and method of moments (MoM). The hybrid scheme has been designed to handle complex geometries comprising arbitrary thin-wire structures and inhomogeneous dielectric regions the shape of which can also be arbitrary. Numerical results are presented which illustrate the accuracy of the method     

Multiport network description and radiation characteristics ofcoupled dielectric resonator antennas

An efficient procedure is presented to investigate the mutual coupling effects and radiation characteristics of dielectric resonator (DR) antennas operating in an array environment. The procedure is based on the method of moments (MoM) as applied to a system of surface integral equations (SIEs) for the coupling of a dielectric body of revolution (BOR) to a nonBOR geometry. The antenna array elements are situated on a ground plane and fed by coaxial probes. Multiport network impedance parameters computed by this method show good agreement with those obtained by measurement. Computed driving point impedances are given for arrays exhibiting optimum pattern performance in terms of low cross polarization and good pattern symmetry     

Rapid calculation of the Green's function in a rectangular enclosure with application to conductor loaded cavity resonators

A new technique for rapid calculation of the Green's functions in a rectangular cavity is presented. The method is based on a best polynomial approximation in three dimensions, which is implemented through a fast cosine transform. Generating the required samples for polynomial modeling is greatly accelerated through Ewald summation technique. To validate the efficiency of the resulting Chebyshev series for the potential Green's functions, a surface integral-equation (SIE) formulation is used to compute the resonant frequency of conductor loaded cavity resonators. The new scheme is proved to be considerably faster than Ewald transform in filling the method of moments (MoM) matrix. A SIE with the MoM can now be efficiently used for electromagnetic analysis and optimization of conductor or dielectric loaded resonators and filters with rectangular enclosures.     

Analysis of the electromagnetic inductive response of a void in aconducting-soil background

A lossless dielectric object situated in a lossy dielectric medium (soil) constitutes a void in a conducting background, which can be detected via an electromagnetic-induction (EMI) sensor operating at appropriate frequencies. The electromagnetic character of this void is dependent on the target and soil properties, as well as on the frequency of operation. We utilize the rigorous method of moments (MoM) and the approximate extended-Born technique to model this three-dimensional (3-D) problem. The modeling algorithms are discussed in detail, with a focus on efficient computation of the dyadic Green's function at the frequencies of interest. The MoM results are used to calibrate the accuracy of the approximate extended-Born solution, over a wide range of operating conditions. Furthermore, the computer simulations are used to perform a detailed phenomenological study     

Hybrid PO-MoM analysis of large axi-symmetric radomes

Over the last three decades, intensive work has been done to develop techniques aimed at accurate and efficient analysis of antenna radome systems. Some applications involve radar operating in the millimeter wave range and for those cases the radome size can be on the order of one hundred wavelengths or so in length. For practical simulations of such large radomes, a hybrid physical optics-method of moments (PO-MoM) technique is presented for accurate and efficient analysis of electrically large radomes. The procedure combines the method of moments (MoM) for modeling the tip region of the dielectric radome and ray optics in conjunction with physical optics (PO) for treating the flatter smooth section of the radome. Calculated far-field patterns using the new technique agree well with measured data for a reflector antenna radiating in the presence of a large radome. The computational time for simulating the performance of a 46λ reflector in the presence of an 88λ long radome was a mere 4 h on a 233 MHz PC     

A fast MoM calculation technique using sinusoidal basis and testing functions for a wire on a dielectric substrate and its application to meander loop and grid array antennas

The input impedance matrix element of the method of moments (MoM) for an arbitrarily shaped wire antenna printed on a dielectric material Z/sub m,n/ is formulated to be composed of three terms Z/sup /spl psi/s//sub m,n/, Z/sup /spl psi///sub m,n/, and /spl Delta/Z/sub m,n/ involving single-, double-, and triple-integral calculations, respectively. The MoM based on the Z/sub m,n/ formulated in this paper (new MoM) is applied to two antennas-a meander loop antenna and a grid array antenna-as well as a simple loop used as a reference antenna. The computation time to obtain the current distribution of each antenna by the new MoM technique is compared with the time required for the conventional MoM, which has an impedance matrix element composed of four terms, all involving triple-integral calculations. It is revealed that the new MoM drastically reduces the computation time: for example, by a factor of 937 for the grid array antenna. In addition, the radiation characteristics of these two antennas are discussed. It is found that a reduced-size meander loop (62% smaller than the simple loop reference) has a radiation pattern similar to the simple loop reference. It is also found that the grid array has an axial beam radiation pattern without side lobes in the principal planes.     

Printed antennas analysis by a Gabor frame-based method of moments

Gabor frame-based discretization is proposed for the first time as a fully rigorous and flexible tool in the context of antenna analysis. A rigorous discretization procedure based on frame theory is presented and applied to integral equations solution through a method of moments (MoM). In this approach, the unknown field or current is expanded in a set of spatially and spectrally translated elementary functions. The use of a Gaussian window function as basis element allows for the representation of radiated fields as a superposition of shifted and rotated Gaussian beams. By exploiting the well understood propagation and transformation features of Gaussian beams, the fields can be evaluated by summations of analytic terms, at any observation point. This method seems well suited to model antennas embedded in complex systems including arbitrary interfaces. Numerical results are presented for slot antennas at the interface between two dielectric half spaces and compared to a standard MoM to validate the approach and illustrate its attractive characteristics.     

二维电大导体目标宽带雷达散射截面的快速计算

在矩量法的基础上,应用空间分解技术将二维电大导体目标剖分成若干子区域,考虑子区域间的耦合,通过累进迭代法计算出目标表面电流,然后结合渐近波形估计技术计算了二维电大导体目标的宽带雷达散射截面.数值计算表明:计算结果与矩量法逐点计算结果相吻合,计算效率大大提高.     

Forward-backward method for scattering from dielectric rough surfaces

The iterative forward-backward (FB) method is a recently proposed efficient technique for numerical evaluation of scattering from perfectly conducting rough surfaces. Extension of the method to include scattering from imperfect conducting surfaces, with a high imaginary part of the complex dielectric constant, has also been proposed. The FB method is further generalized to analyze scattering from dielectric rough surfaces with arbitrary complex dielectric constant. Electric and magnetic equivalent surface currents are split into forward and backward components and equations governing these current components are obtained. As a solution, an iterative scheme is proposed and its convergence rate is analyzed. Finally, the effectiveness of the method is assessed by comparing the obtained scattering results with "exact" ones, computed by employing the usual method of moments (MoM).     

Rigorous Analysis of Rectangular Dielectric Resonator Antenna With a Finite Ground Plane

A probe-fed rectangular dielectric resonator antenna (RDRA) placed on a finite ground plane is numerically investigated using method of moments (MoM). The whole structure of the antenna is exactly modeled in our simulation. The feed probe, coaxial cable and ground plane are modeled as surface electric currents, while the dielectric resonator (DR) and the internal dielectric of coaxial cable is modeled as volume polarization currents. Each of the objects is treated as a set of combined field integral equations. The associated couplings are then formulated with sets of integral equations. The coupled integral equations are solved using MoM in spatial domain. The effects of ground plane size, air gap between dielectric resonator and ground plane, probe length, and position on the radiation performance of the antenna including resonant frequency, input impedance, radiation patterns, and bandwidth are investigated. The results obtained for the antenna parameters based on the MoM investigation shows that there is a close agreement with those obtained by measurement. Moreover it is shown that the MoM results are more accurate than other simulation results using software package such as High Frequency Structure Simulator (HFSS).      

Analysis and measurement of mode polarizers in square waveguide

A general analysis approach for strip metallization structures enclosed in rectangular or square waveguide is presented. The technique involves the novel application of a commercially available 2.5-dimensional (2.5-D) method-of-moments-based (MoM) electromagnetic (EM) analysis tool to a three-dimensional (3-D) waveguide problem. Very good agreement is demonstrated between computed and measured results for several printed strip linear polarizers embedded within a square waveguide environment. This paper, to the authors' knowledge, represents the first such comparison of phase and magnitude between computed and measured data for strip grid polarizers in a waveguide environment. The developed approach involves construction of a theoretical waveguide “test fixture” and an associated theoretical de-embedding procedure. Computational advantages are expected over the alternative approach of using a finite-element-based fully 3-D analysis approach. The polarizer results have potential application to shielded versions of quasi-optic array components that have been demonstrated in open geometries, as well as to multimode antenna feeds, waveguide filters, and matching networks     

Efficient Analysis of Phased Arrays of Microstrip Patches Using a Hybrid Generalized Forward Backward Method/Green's Function Technique With a DFT Based Acceleration Algorithm

A hybrid method based on the combination of generalized forward backward method (GFBM) and Green's function for the grounded dielectric slab together with the acceleration of the combination via a discrete Fourier transform (DFT) based algorithm is developed for the efficient and accurate analysis of electromagnetic radiation/scattering from electrically large, irregularly contoured two-dimensional arrays consisting of finite number of probe-fed microstrip patches. In this method, unknown current coefficients corresponding to a single patch are first solved by a conventional Galerkin type hybrid method of moments (MoM)/Green's function technique that uses the grounded dielectric slab's Green's function. Because the current distribution on the microstrip patch can be expanded using an arbitrary number of subsectional basis functions, the patch can have any shape. The solution for the array currents is then found through GFBM, where it sweeps the current computation element by element. The computational complexity of this method, which is originally ( being the total number of unknowns) for each iteration, is reduced to using a DFT based acceleration algorithm making use of the fact that array elements are identical and the array is periodic. Numerical results in the form of array current distribution are given for various sized arrays of probe-fed microstrip patches with elliptical and/or circular boundaries, and are compared with the conventional MoM results to illustrate the efficiency and accuracy of the method.