Point Matching Moment Method Research Articles

Analysis of Thin Truncated Cylinder Scatterers Using Incomplete Hankel Functions and Surface Impedance Boundary Conditions

The incomplete Hankel functions (IHFs) are employed to evaluate the scattered field from thin truncated cylinders excited by uniform plane waves or by arbitrarily oriented elemental current sources. Metallic and dielectric lossy structures are modeled by means of impedance boundary conditions (IBCs) including surface curvature effects. The scattering currents, expanded in triangular basis functions, are determined upon solving electrical field integral equations (EFIEs) by means of the point-matching method of moments (MoM). The scattered field is then expressed in closed analytical form in terms of IHFs, thus yielding highly accurate numerical results. Furthermore, accurate IHFs approximants are also derived to reduce the computational burden in the analysis of large electrical structures. The proposed approach is demonstrated in practical applications involving cylindrical dielectric structures used in planar lenses, lossy dielectric cylinders suitable to model cane-like vegetation, as well as polarization rotators featuring multiple stages composed of thin metallic wire arrays.

Maxwell Garnett theory limitations in the analysis of bi‐anisotropic composites

The constitutive parameters of metamaterials composed of asymmetrical inclusions are inaccurate when calculated using Maxwell Garnett theory. In this study, the authors discuss some particular cases of metamaterials composed of asymmetrical inclusions to demonstrate this statement. The unit cell single element dyadic is derived numerically using the induced currents by incident plane waves and is computed by point matching method of moments. The composite effective parameters approximated by Maxwell Garnett model were used to obtain the reflection and transmission coefficients from a bulk slab. The derived results were compared to the simulated numerical results with High Frequency Structure Simulator (HFSS) software. The scattering parameters from symmetrical and asymmetrical inclusions were compared and a parametric study was conducted. The scattering parameters are in good agreement when the material under consideration is composed of symmetrical inclusions and hold even for higher frequencies than Maxwell Garnett model theory limits. For asymmetrical inclusions the model provides inaccurate scattering parameters results. This discrepancy is especially pronounced when the illuminating field polarisation coincides with the inclusion asymmetry direction. These observations should be considered when Maxwell Garnett model is used for effective parameters analytical approximation.

The analysis of monopole antenna centered on circular ground plane using boundary diffraction wave

AbstractVarious methods for the analysis of a monopole antenna located on a perfectly conducting circular ground plane have been proposed as a canonical electromagnetic field problem and as a model for an antenna used for wireless communications. On the other hand, the physical optics approximation has been used as a powerful method for the electromagnetic scattering problems and the problem of representation of radiation patterns of antennas. As an example of application of this physical optics approximation, the effect of the scattered waves generated by the presence of a circular ground plane is expressed by the boundary diffraction wave in this paper and an analysis of the above problem is attempted. For the scattering wave representation using the boundary diffracted wave, the current distribution on the antenna is derived by the point matching method of moments and the input impedance characteristics and the radiation patterns are calculated. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 88(4): 54–63, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20152

Surface currents induced on a dielectric half‐space by a Gaussian beam: An extended validation for point matching method of moment codes

An approximate analytical solution for electric surface currents induced on a planar dielectric half‐space by a normally incident Gaussian beam is presented. This solution provides a useful tool for testing discretization methods in point matching moment method codes for penetrable rough surface scattering which use a Gaussian beam “tapered” incident field to avoid edge effects. For one example case illustrated, the surface current solution obtained can be shown to satisfy standard impedance boundary condition integral equations at the beam center to within 0.01% accuracy, and a separation of individual term contributions to the entire integral equation enables a detailed check of moment method discretization procedures to be performed.

Surface Voltages and Resistance of Grounding Systems of Grid and Rods in Two-Layer Earth by the Rapid Galerkin's Moment Method

The point matching moment method has been the prime candidate for grounding system analysis. The regular method yields accurate results as long as the segmentation is very fine. This means a large number of basis functions and frequently requires a super computer. In the present paper, we propose an alternate moment method in the Galerkin's form. This form is variational (i.e. with error reduction property) which allows for very few basis functions, resulting in a very fast convergence but still gives less than 2% error in the grounding resistance. Each basis function in this form can be a whole rod with uniform current distribution, representing a vertical driven rod or a horizontal rod across a whole grid. Such basis functions give good results in the grounding resistance, it is obvious that they need not give good results in the voltages (ground potential rise, touch, and step) on the earth surface near the grid intersections. To correct this, a second type of basis functions namely spheres is added at the intersections. Since the intersections are few, the total number of basis functions is still small. With such basis functions added, however, the resulting voltages now have errors generally less than 4%. With such high accuracy and small matrix size (/spl ap/10/spl times/10 to 50/spl times/50) in the moment method it is easy to do parametric studies, even for an extensive grounding system.

Surface voltages and resistance of grounding systems of grid and rods in two-layer earth by the rapid Galerkin's moment method

The point matching moment method has been the prime candidate for grounding system analysis. The regular method yields accurate results as long as the segmentation is very fine. This means a large number of basis functions and frequently requires a super computer. In the present paper, we propose an alternate moment method in the Galerkin's form. This form is variational (i.e. with error reduction property) which allows for very few basis functions, resulting in a very fast convergence but still gives less than 2% error in the grounding resistance. Each basis function in this form can be a whole rod with uniform current distribution, representing a vertical driven rod or a horizontal rod across a whole grid. Such basis functions give good results in the grounding resistance, it is obvious that they need not give good results in the voltages (ground potential rise, touch, and step) on the earth surface near the grid intersections. To correct this, a second type of basis functions namely spheres is added at the intersections. Since the intersections are few, the total number of basis functions is still small. With such basis functions added, however, the resulting voltages now have errors generally less than 4%. With such high accuracy and small matrix size (/spl ap/10/spl times/10 to 50/spl times/50) in the moment method it is easy to do parametric studies, even for an extensive grounding system.

Application of a point-matching MoM reduced scheme to scattering from finite cylinders

One of the most common methods for the solution of three-dimensional (3-D) scattering problems is the electric-field volume integral equation numerically solved by the application of the method of moments (MoM)-usually the point-matching version. Although simple to formulate, it shows inherent difficulty and complexity because of the 3-D integrals appearing in the interaction matrix elements and of the singularity of the dyadic Green's function (DGF) present in the computation of the self-cell elements. In this paper, a transformation method is presented, which in the case of the point-matching MoM, both reduces the 3-D integrals to two-dimensional (2-D) ones, and also eliminates the need of separate treatment of the singularity while maintaining the same degree of approximation. Comparison to published results is made for the case of scattering by a finite dielectric cylinder. Further examples are presented for scattering by layered dielectric cylinders and lossy cylindrical shells excited by uniform plane waves.

A fast and accurate analysis of grounding resistance of a driven rodbed in a two-layer soil

A moment method of the Galerkin (variational) approach is applied to analyze the grounding resistances of driven rodbed of various configurations. Using this approach the resistance of a rodbed of N rods in two-layer soil requires only a matrix size of 2N/spl times/2N (two segments for each rod). The error in the calculated resistance is less than 4% compared to the resistance calculated by point matching moment method of large number of segmentation for each rod. The efficiency due to a small matrix with high accuracy allows an extensive parametric analysis of the rodbed. The study shows that a precise placement of the rods is not necessary to maintain a given resistance.

Efficient computation of rodbed grounding resistance in a homogeneous earth by Galerkin's moment method

This paper computes the grounding resistance of rodbeds in a homogeneous earth by a moment method with Galerkin's approach. The self and mutual resistances matrix result is quite small. It shows that an N rod assembly requires only an N/spl times/N matrix. The resistance of the rodbed grounding system calculated using this method has a percentage difference of less than 2% from the point matching moment method. Galerkin's moment method does not match the boundary potential at one point of a segment, but matches the boundary potential that is averaged over the whole segment. Such a simple change in the moment method makes the method variational and results in a very small error even with a substantial saving in computation effort. The effects of various system parameters on the rodbed parameters (such as rod sunken depth, rod length and radius, rod spacing, rodbed configuration, and number of the rods) are investigated and discussed in detail. The paper ends with a discussion on the accuracy of the surface ground potentials with the coarse segmentation of one segment per rod.

Scattering by a chiral cylinder of arbitrary cross section

An integral equation and method-of-moments (MM) solution to the problem of scattering by an inhomogeneous chiral cylinder of arbitrary cross section is presented. The volume equivalence theorem for chiral media is developed and used to formulate a set of coupled integral equations for the electric and magnetic volume polarization currents representing the chiral cylinder. These coupled integral equations are solved using a standard pulse basis and point-matching MM solution. Numerical results, including echo width and internal fields, are presented for the scattering by chiral slabs and circular cylinders. These results are compared to exact solutions when available.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>