Frequency-domain Method Of Moments Research Articles

A Marching-on-in-Time Method of Moments for Transient Modeling of a Vertical Electrode Buried in a Lossy Medium

This article proposes a full-wave time-domain method for analyzing the transient behavior of a grounding electrode buried vertically in a lossy soil. In this method, the electrode is first approximated by a thin wire, and the modified image theory is utilized to account for the soil–air interface. The governing electric field integral equation (EFIE) is then derived with the current distribution along the electrode being the unknown quantities. Finally, the EFIE is solved by the time-domain method of moments based on a marching-on-in-time (MOT) procedure. This is done by expanding the unknown currents in terms of a finite linear combination of products of appropriate spatial and temporal basis functions, and adopting the Galerkin method in space and the point matching method in time. The MOT procedure makes the proposed method more efficient computationally than its rival frequency-domain method of moments (FD-MoM). The efficiency of the proposed method is demonstrated by comparing the lightning ground potential rise of various grounding electrodes with those obtained using the FD-MoM and a commercial numerical code.

Supplements to “A Time-Domain Macromodel Based on the Frequency-Domain Moment Method for the Field-to-Wire Coupling”

A macromodel method based on the method of moments was proposed in a previous paper to efficiently and statistically analyze the field coupling to thin-wire structures of arbitrary shape in free space or above the perfectly conducting ground. Through numerical tests and physical insights, it was shown that the extracted macromodel is irrelevant to the port impedances. In this correspondence, a rigorous mathematical derivation is given to prove the irrelevance. The work completes the macromodel method and constitutes its theoretical foundation.

A STUDY ON THE NUMERICAL ACCURACY OF THE MATRIX ELEMENTS IN A TIME DOMAIN MOD METHODOLOGY

In a time domain Marching-on-in-degree (MOD) solver based on a Galerkin implementation of the Method of Moments (MoM), it is observed that the matrix elements for the matrix to be inverted contain integrals that are similar to the ones encountered in a frequency domain MoM solver using the piecewise triangular patch basis functions. It is also observed that the error in the evaluation of the matrix elements involving these integrals are larger in the time domain than those involved in the frequency domain MoM solvers. The objective of this paper is to explain this dichotomy and how to improve upon them when using the triangular patch basis functions for both the time and the frequency domain techniques. When the distance between the two triangular patches involved in the evaluation of the matrix elements, are close to each other or when the degree of the Laguerre polynomial in a MOD method is high, the integral accuracy will be compromised and the number of sampling points to evaluate the integrals need to be increased. Numerical results are presented to illustrate this point.

Comments on "Fast direct solution of method of moments linear system

In the above-named work a new algorithm is presented for direct (non-iterative) frequency domain method of moments (MoM) calculations based on block-wise compression of the impedance matrix. The storage requirements and computational complexity of the algorithm are claimed to be N3/2 and N2, respectively, if N is the number of unknowns for a MoM surface discretization that is fixed with respect to the wavelength. A more rigorous analysis, explicitly using the asymptotic expression for the number of degrees of freedom (DoF) in the interaction between groups of scatterers, is presented here, showing that this should be N3/2log N and N2log2 N, respectively. The complexity analysis applies to problems that can be formulated as a surface integral equation (SIE) on surfaces in or between homogeneous media, such as a ship or an airplane. It does not apply to volume discretization MoM or multilayer problems. The results presented here are also relevant for block-wise compression methods using iterative solvers, since the compressed impedance matrix is the same. Consequently, the above complexity analysis applies to very large problems, well beyond the reach of even the largest existent computers. For moderate size problems, the measured complexity is lower.

A note on using the frequency-domain moment method for rectangular microstrip antennas

This paper presents simple numerical techniques for solving integrals involving products of two Bessel functions. Such techniques help the convergence of integrals used in the frequency-domain moment method, when the basis functions are Bessel functions of order zero (such as those normally used for rectangular microstrip antennas). Several other electromagnetic problems can benefit from these techniques. Bessel functions and their possible integrals are widely available in the literature, but these materials always target mathematicians and not engineers. The solution of the numerical integral depend on the complexity of the other functions that compose the integrand (Green's function), but certainly the techniques presented here can help

Estimation of Equivalent Circuit of Loaded Trans-receive Antenna System and its Time Domain Studies

The time domain studies of different reduced-height loaded wire antennas (e.g., inverted L, T, I and C-shaped antennas) when used in trans-receive system is presented. Due to the reduced height of the loaded antennas, these antennas have found wide application as transmitting and receiving antenna/sensors for electromagnetic interference (EMI) measurements. However, while using these antennas in trans-receive system for wideband application, the time domain characterization of both the transmit and receive antenna is required and investigation on this has not yet been performed. This paper presents the results of the initial investigation on the time-domain performance of these loaded trans-receive systems. An optimized transmit antenna generator waveform is used to maximize receive antenna voltage amplitude (with bounded input energy), as presented in the recent literature. The frequency domain Method of Moments with Pulse basis function and Point-matching technique has been used to evaluate the current distribution on the antenna surface and hence the radiated electric field at the position of the receiving antenna. The same technique has been extended for receiving wire antenna to evaluate the Complex Antenna Factor (CAF) of these antennas. The CAF versus frequency data has been used to evaluate the input and output voltage waveform of the trans-receive system. The results have been verified with theoretical and experimental data available in reported works.

SAR and radiation performance of balanced and unbalanced mobile antennas using a hybrid computational electromagnetics formulation

A procedure to reduce the effect of the mobile antenna on the handset by using balanced antennas has been investigated. Use of this type of antenna may degrade the antenna performance, such as bandwidth and gain, although it can cause less effect on the body to which they are adjacent. If the antennas are well designed, the maximum specific absorption rate (SAR) values are likely to be reduced when placed next to the head, since the coupling of such antennas to the body of the handset is very weak. A study on balanced and unbalanced antennas for mobile handsets next to the human head is presented, using a hybrid electromagnetics method for the analysis. The method uses the hybridisation technique between the frequency-domain method of moments (MoM) and the finite-difference time-domain method (FDTD). The antenna was modelled using MoM whereas the head tissues were modelled using FDTD. Two antennas were designed and investigated with respect to the SAR and radiation performance for two different antenna positions on the top edge of a mobile handset. Radiation patterns are presented and compared, with and without the head, and the maximum SAR values and field distributions inside the head are discussed. The balanced antenna shows good improvements with respect to the unbalanced antenna in terms of the SAR values and variations of the input impedances.

Resolution and polarization in apertureless near-field microscopy

We present numerical calculations of the electromagnetic fields produced around a sharp metal tip held above a dielectric surface and illuminated from above by visible light. This geometry is that of an apertureless near-field scanning optical microscope (A-NSOM). The electric fields produced by irradiation are calculated using a real-space Green’s function technique, also known as the frequency-domain method of moments. We investigate numerically the convergence properties of this method with respect to the grid size used to discretize the equations and find that the usual criterion invoked to ensure convergence does not apply inside small metallic scatterers; for this reason, the fields near the border of the tip keep changing as we make the grid smaller and smaller. Although the calculations do not show convergence (for the intensity of the fields near the borders of the probe), the intensity and the polarization of the field in other regions of space are converged; they do not change as the grid spacing is made smaller. When the tip is five nanometers above a flat dielectric surface the field under the tip is strongly enhanced in a region having a diameter of five nanometers, even though the end of the tip has lateral dimensions of order ten nm. The light intensity falls off rapidly as the tip–surface separation is increased and the region where the field is enhanced becomes larger. This implies that illuminating very small areas with this device requires very good control of the tip height. Most of the results presented here are for an Al tip, but we have also performed calculations for tips made of sapphire, gold, silver, and tungsten. For all probes, the field localization, and hence the NSOM resolution, depends only weakly on the tip composition, whereas the magnitude of light intensity enhancement is strongly dependent on the dielectric properties of the tip. When the probe is very close to the surface, giving the best lateral resolution, the spatial variation of the electric field near the surface is quite complicated, and is different for different components of the electric field vector; the polarization of the field under the tip is not the same as the polarization of the incident far field or that of the field in the absence of the tip. Regardless of the incident polarization, the tip tends to make the induced electric field perpendicular to the substrate. Moreover, different components of the field have different spatial distributions; knowing the orientation of the field creates the possibility of deducing the orientation of molecules adsorbed on the surface.

SEM representation of transient scattering from conducting planar objects in layered media

The scattering of a plane wave from conducting planar objects in layered media has been analysed by a frequency-domain method of moments (MoM) with rooftop basis functions and Galerkin's procedure. Green's functions for layered media involved in the computation of the matrix elements are evaluated using the closed-form expressions obtained from the robust approach using the generalised pencil-of-function (GPOF) method. The time-domain scattered field from the scatterer illuminated by an electromagnetic pulse is obtained from its frequency-domain data via the inverse fast Fourier transform (FFT). The poles and residues of the time-domain response are then extracted via the GPOF method. The singularity expansion method (SEM) representation of the time-domain response using the poles and residues is finally obtained. The pole locations in a complex frequency plane as a function of the substrate thickness, relative dielectric permittivity and dielectric loss are also investigated. Complex natural resonances for a microstrip dipole and patch are sufficiently diverse for identification purposes, thus demonstrating that only pole and residue information is required for target characterisation.

Complex Resonant Frequencies for the Identification of Simple Objects in Free Space and Lossy Environments - Abstract

The frequency-domain method of moments (MoM) has been used to analyze the induced current characteristics for an arbitrarily shaped, perfectly conducting, thin wire antenna and scatterer. The time-domain response of the current is obtained from the frequency domain data via an inverse fast Fourier transform (FFT) when the wire is excited by a Gaussian pulse. The numerical results of the transient current show that the late-time responses for both the radiation and scattering of a straight wire are almost identical, but that their early-time responses are quite different. The poles and residues of the time-domain response that contain the complex resonant frequencies of the scattering object are then extracted via the generalized pencil-of-function (GPOF) method. It is numerically demonstrated that the complex resonant frequencies of the object are their natural frequencies since they do not depend on the excitation sources. The time-domain response reconstructed by using the poles and residues is in excellent agreement with that obtained by FFT of the frequency domain data. The complex resonances for the transient scattering of an L-shaped wire are also analysed. As an application of this method to the radiation and scattering of buried bodies, the scattering from a strip on the surface of a lossy half-space is investigated and its complex resonances are recognized.

Numerical algorithms for the hypercube concurrent processor

With the development of concurrent computing architectures which promise cost-effective means of obtaining supercomputing performance, there is much interest in applying and in evaluating the actual performance on large, computationally-intensive problems. Of particular interest is the concurrent performance of large scale electromagnetic scattering problems. Two electromagnetic codes with differing underlying algorithms have been converted to run on the Mark III Hypercube. One is a time domain finite difference solution of Maxwell's equations to solve for scattered fields and the other is a frequency domain moment method solution. Important measures for demonstrating the utility of the parallel architecture are the size of the problem that can be solved and the efficiency by which the paralleling can increase the speed of execution.

A hybrid moment method/finite-difference time-domain approach to electromagnetic coupling and aperture penetration into complex geometries

An approach is presented for the direct modeling of electromagnetic penetration problems which involves a hybrid technique combining the frequency-domain method of moments (MM) and the finite-difference time-domain (FD-TD) method. The hybriding is based upon a novel use of a field equivalence theorem due to Schelkunoff, which permits a field penetration problem to be analyzed in steps by treating the relatively simple external region and the relatively complex internal region separately. The method involves first, determination of an equivalent short-circuit current excitation in the aperture regions of the structure using MM for a given external illumination. This equivalent current excitation over the aperture is next used to excite the complex loaded interior region, and the penetrating fields and induced currents are computed by the FD-TD method. A significant advantage of this frequency domain/time domain hybriding is that no Green's function need be calculated for the interior region. This hybrid approach takes advantage of the ability of MM to solve exterior problems using patch models and also takes advantage of the ability of FD-TD to model in great detail localized space regions containing metal structures, dielectrics, permeable media, anisotropic or nonlinear media, as well as wires.