Method Of Moments Formulation Research Articles

Beam steered reactively loaded printed microstrip loop antennas

Printed microstrip loop antennas loaded with reactive components are analysed to demonstrate the capability of beam steering by reactance adjustment. The geometry of the printed microstrip loop including reactive element loading is represented as a superquadratic function so that the current distribution, hence radiation pattern for various antenna loop shapes, can be calculated using a unified method of moment formulation. The effects of the loop shapes and dielectric substrates on the beam steering capability and input impedance characteristics are investigated. It is found that continuous beam steering can be achieved and that a compromise has to be made between the maximum beam steering and minimum input VSWR. A 1.0GHz experimental verification is provided, which demonstrates that beam steering of 24/spl deg/ can be achieved by control of a single reactive element, while low cross-polarisation (/spl sim/ -20 dB) and VSWR (/spl sim/ 1.7) can be simultaneously maintained.

Physics‐based preconditioner for iterative algorithms in multi‐scatterer and multi‐boundary method of moments formulations

AbstractAn efficient method to solve electromagnetic scattering problems involving several metallic scatterers or bodies composed of dielectric and metallic regions is proposed. So far, the method of moments has successfully been applied to large arrays of identical scatterers when it was combined with preconditioned iterative algorithms to solve for the linear system of equations. Here, the method is generalized to geometries that are composed of several metallic elements of different shapes and sizes, and also to scatterers that are composed of metallic and dielectric regions. The method uses in its core an iterative algorithm, preferably the transpose‐free quasi‐minimum residual (TFQMR) algorithm, and a block diagonal Jacobi preconditioner. For best performance, the blocks for the preconditioner are chosen according to individual scatterers or groups of scatterers for the array case, and according to the electric and magnetic current basis functions for dielectric/metallic scatterers. The iterative procedure converges quickly for an optimally chosen preconditioner, and is robust even for a non‐optimal preconditioner. Reported run times are compared to run times of an efficiently programmed LU factorization, and are shown to be significantly lower. Copyright © 2002 John Wiley & Sons, Ltd.

Transfer impedance of nonmagnetic conduits of various shapes

Metallic conduits provide mechanical support for cables, and may also protect the cables against interference caused by currents induced by external electromagnetic fields. The conduit transfer impedance Z/sub t/ then is a good measure for the provided protection. We studied Z/sub t/ by means of conformal transformations and of the method of moments in a quasistatic, two-dimensional (2-D) approach. Practical U-, H-, L-, and T-shaped conduits are discussed. Conformal transformations provide simple engineering expressions for the mutual inductance part of Z/sub t/ for cable positions inside the conduit. The method of moments formulation results in useful approximations for the crossover frequencies in Z/sub t/ between DC and high frequency. Measurements on U-shaped conduits confirm the calculations.

Numerical simulation of scattering from rough surfaces: a wavelet-based approach

In this paper, a preliminary study is carried out to demonstrate the application of wavelets for improving the computation time and reducing computational memory required for evaluating the statistics of the scattered field from rough surfaces using the method of moments (MoM) in conjunction with a Monte Carlo simulation. In specific, Haar and the first order B-spline wavelet basis functions are applied to the MoM formulation of one-dimensional rough surfaces in order to compare the computation time and sparsity for wavelets in the same family but of higher order. Since the scattering coefficient (the second moment of the backscatter field per unit area) is a gentle function of the surface parameters and the radar attributes, it is demonstrated that a relatively high thresholding level can be applied to the impedance matrix, which leads to a sparser impedance matrix and faster computation time. It is also shown that applying a high threshold level the coefficients of the high-order wavelets would increase out of proportion, however, the effect of these current components averages out when computing the scattering coefficients. The resulting sparse impedance matrices are solved efficiently using fast search routines such as the conjugate gradient method. A systematic study is carried out to investigate the effect of different threshold levels on the accuracy versus computing speed criterion. The computed scattering coefficients are compared to previous results computed using a conventional pulse basis function as well as the existing theoretical solutions for rough surfaces. It is shown that wavelet basis functions provide substantial reductions in both memory requirements and computation time.

Efficient evaluation of spatial-domain MoM matrix entries in the analysis of planar stratified geometries

An efficient hybrid method for evaluation of spatial-domain method-of-moments (MoM) matrix entries is presented in this paper. It has already been demonstrated that the introduction of the closed-form Green's functions into the MoM formulation results in a significant computational improvement in filling up MoM matrices and, consequently, in the analysis of planar geometries. To achieve further improvement in the computational efficiency of the MoM matrix entries, a hybrid method is proposed in this paper and, through some examples, it is demonstrated that it provides significant acceleration in filling up MoM matrices while preserving the accuracy of the results.

Design of a microwave array hyperthermia applicator with a semicircular reflector.

The design of a hyperthermia applicator for heating biological tissues is presented in which the applicator consists of an array antenna surrounded by a perfect electrically conducting reflector. The heat hazard to superficial tissues is reduced by the introduction of a dielectric protecting layer over them. A method of moments formulation is applied to approximate the electric field within the biological medium and a closed form expression is presented for the electromagnetic coupling problem, which enables an optimisation procedure to be performed. The applicator enhances both penetration and focusing: deep tumours, close to the bone region, are heated and the percentage of biologically healthy tissue exposed to a specific absorption rate (SAR) hazard level diminishes by 53.8%.

A fast integral equation approach to acoustic scattering from three-dimensional objects using a natural basis set

Boundary value integral equations and the moment method solution technique provide a succinct and elegant strategy for the solution of acoustic surface scattering problems. This paper explores the application of a subdomain basis set, based on the phase of the incident radiation, which is used to solve for the unknown normal pressure gradient on the surface of the scatterer using the moment method. The advantage of this basis set lies in the fact that it can accurately represent the fast phase character of the pressure gradient on the surface of the scatterer. This allows for far fewer discretizations/basis elements in the moment method formulation and therefore significantly reduces the density of unknowns that must be numerically computed. The main contribution of this paper is to show how to efficiently employ this natural basis and to explore the physical justification for using this approach. The method is compared with other techniques including the Kirchhoff solution technique, high frequency single scattering techniques, the Nussenzveig–Fock technique, and the parabolic equation approximation. Unlike these methods no approximation to the physical system need be introduced.

A method of moments approach for the efficient and accurate modeling of moderately thick cylindrical wire antennas

This paper introduces a moment-method formulation, which is capable of accurately modeling moderately thick cylindrical wire antennas. New algorithms are presented for the efficient computation of the cylindrical wire kernel and related impedance matrix integrals. These algorithms make use of exact series representations as well as efficient numerical procedures and lead to a significant reduction in overall computation time for thicker wires. Another major advantage of this moment-method technique is that it is no longer restricted by the segment length-to-radius ratio limitations inherent in past formulations, thereby making it possible to achieve solution convergence for a much wider class of wire antenna structures. Several examples illustrating the superior convergence properties of this new moment-method formulation are presented and discussed.

Analysis of a slot-coupled T-junction between circular-to-rectangular waveguide

This paper presents a rigorous analysis of a slot-coupled T-junction between a primary circular cylindrical waveguide and rectangular waveguide, forming the coupled T-arm. The analysis is based on moment-method formulation using full-wave basis functions and Galerkin's technique for testing. Expression for the coupling and reflection coefficients are found, taking into account the effect of finite wall thickness of the circular waveguide in which the coupling slot is milled. A comparison between the theoretical and experimental results on coupling and return loss are presented.

Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies

We present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of the CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ the MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects.

Efficient use of closed-form Green's functions for the analysis of planar geometries with vertical connections

An efficient and rigorous method for the analysis of planarly layered geometries with vertical metallizations is presented. The method is based on the use of the closed-form spatial-domain Green's functions in conjunction with the method of moments (MoM). It has already been demonstrated that the introduction of the closed-form Green's functions into the MoM formulation results in significant computational improvement for the analysis of planar geometries. However, in cases of vertical metallizations, such as shorting pin's, via holes, etc., there are some difficulties in incorporating the closed-form Green's functions into the MoM formulation. In this paper, these difficulties are discussed and their remedies are proposed. The proposed approach is compared to traditional approaches from a theoretical point of view, and the numerical implementation is demonstrated through some examples. The results are also compared to those obtained from the commercial software em by SONNET.

Moment method formulation for piezoceramic plate vibrations

Presented herein is a numerical algorithm based on the method of moments that has been used recently in structural electroelastic elements [e.g., M. C. Dökmeci and G. A. Altay, Z. angew. Math. Mech. 77, 1–17 (1997) and references therein] in order to predict the dynamic response of a piezoceramic plate. The piezoceramic plate of uniform thickness is coated completely with very thin perfectly conducting electrodes on and under an electric potential applied to its faces. In the first part of the paper, the two-dimensional equations for the piezoceramic plate are derived in both variational and differential forms by use of the differential variational principle [M. C. Dökmeci and G. A. Altay, Int. J. Eng. Sci. 34(7), 769–782 (1996)] together with a series expansion of the field variables. In the second part, the method of moments [M. C. Dökmeci, Proceedings of the 1992 Ultrasonics Symposium (IEEE, New York, 1992), pp. 1025–1028] is described for the dynamic response. The significant mechanical and electrical effects are all taken into account. The equations derived accommodate all the types of motions as well as coupled motions of the piezoceramic plate. In the third part, attention is focused on certain cases involving special geometry, motions, and polarization directions of the piezoceramic plate. [Work supported in part by TÜBA.]

A moment method approach using frequency-independent parametric meshes

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.

The Coupling of Fourier Series With Method of Moments To Solve Poisson Type Equations

A method for handling the non-homogeneous terms occurring in the method of moments formulation of the Poisson equation is proposed. The algorithm is based on using the Fourier series expansions for solving the general two-dimensional Poisson equation without the need for either domain discretization nor Monte Cario integration techniques. The convergence of the present method is studied and improved by using the algorithm. Application of this method to the determination of the depletion layer profile is presented along with several other engineering problems. The results are compared with solutions available in the literature.

A New Efficient Moment Method Formulation for the Design of Microstrip Antennas Over a Chiral Grounded Slab

An arbitrarily shaped microstrip patch antenna excited by a three-dimensional electric point-source is examined. The metallic patch resides on a biisotropic chiral grounded slab. The analysis is based on the integral equation approach. The Green functions for the layered medium are used to formulate a coupled set of integral equations for the patch induced current. The layered medium Green dyadic function is expressed in terms of spectral TE and TM waves and of Sommerfeld-type integrals. The Sommerfeld-type integrals are expressed in a new and original way which greatly reduces the computational effort. Simulation results for structures in various high frequency configurations are presented.

Numerical verification of time-domain moment method in ultrasound tomography

In ultrasound tomography the time-domain moment method is very promising in that it has been shown to yield a close agreement between the time-spatial moment expansion and the true field representation. This paper introduces a numerical technique to compute the analytical solution for forward scattering by using a Bessel function series and the inverse discrete Fourier transform, and shows that the artifacts that occur are due to convolution aliasing and undersampling aliasing. Computer simulation has reconstructed these two types of aliasing separately, and has shown that they can be removed by a properly designed algorithm. This alias-free numerical solution is used to verify Cavicchi’s moment-method formulation. A significant improvement in numerical verification is then obtained.

An efficient technique for self-term evaluation of the uniform current vector potential integrals

This communication presents an efficient technique for self-term evaluation of the uniform current vector potential integrals which often arise in certain cylindrical wire method of moments formulations. Simple approximating functions, derived from the application of numerical interpolation routines, are introduced that may be used in place of other more complicated techniques for evaluation of these integrals. In particular, this communication will focus on the development of these approximating functions for application in the moderately thick wire regime, where the reduced kernel approximation associated with thinner wires is no longer valid. It is shown that these proposed functions offer reasonably good accuracy over a wide range of wire segment lengths and radii.

Characteristics of a Vertical Wire Antenna Above a Lossy Earth

The electromagnetic field of a vertical electric dipole in air above a lossy earth (represented by a half space) is studied. An approximate expression for the radial electric field in the half space is derived. Its validity is checked for a selected range of parameters with application to air to subsurface communication. An integral equation for the current on a thin vertical wire antenna kept above the earth is presented. Two moment method formulations are used to solve the integral equation. Numerical results for the antenna impedance from the two solutions are compared. Input impedance and far field pattern are calculated for a half wavelength antenna at varying heights from the air-earth interface for different parameters of the earth.

A transverse slot in the broad wall of inhomogeneously loaded rectangular waveguide for array applications

The self-properties of transverse slots in the broad wall of inhomogeneously loaded rectangular waveguide are computed using an integral equation moment method formulation, and compared to measured values. Results are also presented which show that transverse slots in inhomogeneously loaded rectangular waveguide can be used for antenna arrays which will not have grating lobes in their radiation patterns, and will not suffer from the same distribution taper limitations as similar arrays of homogeneous waveguide transverse slots.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A moment method analysis of a folded E-plane short in rectangular waveguide

A folded E-plane waveguide short is analyzed using a moment method formulation. A comparison of the numerical convergence of the method is shown for two different sets of basis functions: trigonometric aperture waveguide modes and weighted Gegenbauer polynomials. The theory is verified by measurements of a folded short in half-height X-band rectangular waveguide.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>