Thin-wire Electric Field Integral Equation Research Articles

An Envelope-Tracking Hybrid Field-Circuit Simulator for Narrowband Analysis of Nonlinearly Loaded Wire Antennas

An envelope-tracking hybrid field-circuit simulator is proposed for efficiently analyzing narrowband scattering from wire antennas loaded with nonlinear devices. The simulator models the interactions of fields with wires and lumped elements by coupling and simultaneously solving the thin-wire electric field integral equation and Kirchhoff's equations, respectively. The coupled nonlinear system of equations is iteratively solved by a time marching scheme that represents the fields, voltages, and currents of interest (signals) as a truncated series of harmonic sinusoids (carriers) multiplied with complex-valued time-varying coefficients (envelopes). Unlike time-domain simulators, which sample the signals at a rate proportional to their maximum frequency content, the proposed envelope-tracking simulator samples the envelopes at a rate proportional to their maximum bandwidth; thus, it requires significantly fewer time-steps when solving narrowband problems. Moreover, the envelope-tracking simulator is generally more accurate than its time-domain counterpart because of smaller integration and interpolation errors. Numerical results demonstrate that the proposed simulator improves the tradeoff between accuracy and computation time, especially when analyzing antennas excited by narrowband signals or loaded with weakly nonlinear devices.

Direct use of discrete complex image method for evaluating electric field expressions in a lossy half space

A modelling technique is proposed for direct use of the discrete complex image method (DCIM) to derive closed-form expressions for electric field components encountered in the electric field integral equation (EFIE) representing a lossy half space problem. The technique circumvents time consuming numerical computation of Sommerfeld integrals by approximating the kernel of the integrals with appropriate mathematical functions. This is done by appropriate use of either the least-square Prony (LS-Prony) method or the matrix pencil method (MPM) to represent electric field expressions in terms of spherical waves and their derivatives. A comparison is made between the two methods based on the computation time and accuracy and it is shown that the LS-Prony method performs two–three times faster than the MPM in approximating the integral kernels depending on the platform. The main feature of the proposed technique is its ability for direct inclusion in the kernel of computational tools based on the method of moments solution of the EFIE. This can be viewed as an advantage over the conventional DCIM approximation of spatial Green's functions for mixed potential integral equation for cases where the problem in hand can be more efficiently represented by the EFIE (e.g. the thin-wire EFIE). The accuracy of the proposed technique is validated against numerical integration of Sommerfeld integrals for an arbitrary electric dipole inside a lossy half space.

Using MBPE technique to accelerate solving the thin-wire EFIE used in numerical simulation of lightning

The antenna theory (AT) model is widely used to numerically simulate the propagation of current wave along lightning return-stroke channels and compute the radiated electromagnetic fields. In this model, the return stroke channel is considered as a vertical monopole antenna above perfectly conducting ground for which the numerical solution of the governing electric field integral equation (EFIE) in the frequency domain by the conventional method of moment (MoM) is prohibitively slow. In this paper, a model-based parameter estimation (MBPE) technique is proposed to reduce the number of frequency-domain calculation points required for the evaluation of space-time current distribution along a lightning return stroke channel. In applying this technique to a rational function model for the channel current distribution, a uniform-like sampling strategy is investigated. In order to accelerate the building of the moment impedance matrix, the reciprocal closed-form mutual impedance of sinusoidal electric dipoles and the symmetry of the model are used. The proposed technique is validated against the conventional inverse fast Fourier transform algorithm which uses a MoM solution for all frequencies within the channel base current spectrum. It is shown that considerable computation efficiency is achieved in terms of CPU time without losing accuracy.

Analysis of thin-wire ground penetrating radar systems for buried target detection, using a hybrid MoM-FDTD technique

A hybrid method combining the finite difference time domain (FDTD) method and the method of moments (MoM) in the frequency domain is proposed to model the electromagnetic behavior of a realistic ground penetrating radar (GPR) system. The GPR is a non-destructive testing (NDT) technique. It consists of a broadband thin-wire vee-dipole antenna located in the vicinity of a lossy ground containing unexploded ordnances. In the solution of the problem, we identify two sub-problems, namely, the antenna problem and the ground buried object problem. Capabilities of the MoM for solution of the governing thin-wire electric field integral equation of the antenna problem and general FDTD solution of Maxwell's equations posed by the scattering of arbitrary shape objects in multilayered media are combined to efficiently and accurately simulate the electromagnetic operation of the system. The proposed simulation technique is validated against the original MoM solution of the problem. It is shown that the proposed hybrid technique exhibits superior performance based on both computation time and numerical accuracy compared with the conventional FDTD and MoM solution techniques. It is also shown that the position and size of the target, as well as the electromagnetic characteristics of the target, can be determined using a simple signal processing technique.

On the use of piecewise linear wavelets for fast construction of sparsified moment matrices in solving the thin-wire EFIE

Multiresolution wavelet expansion technique has been successfully used in the method of moments (MoM), and sparse matrix equations have been attained. Solving boundary integral equations arising in electromagnetic (EM) problems by the wavelet-based moment method (WMM) involves a time-consuming double numerical integration for each entry of the resultant matrix which in turn can outweigh the advantages of achieving a sparse matrix. The paper presents an alternative computational model to speed up the WMM by excluding double numerical integrations in the evaluation of matrix elements. In this regard, pieces of linear wavelet bases are replaced by proper sinusoidal functions for which closed-form analytical expressions are available. In addition, by introducing approximate closed-form expressions for radiating EM fields of wavelet current elements, the thresholding procedure is modified so that one can compute only the matrix elements of interest. To demonstrate the effectiveness of the proposed method, the thin-wire electric field integral equation (EFIE) is numerically solved by non-orthogonal linear spline wavelet bases.

A fast wavelet-based moment method for solving thin-wire EFIE

Solving the thin-wire electric field integral equation (EFIE) by the multiresolution wavelet expansion method involves a time-consuming double numerical integration for each nonzero element of the moment matrix which in turn can outweigh the advantages of achieving a sparse matrix. To speed up the matrix fill process in wavelet-based moment method codes, first, the triangular scaling functions of a nonorthogonal piecewise liner wavelet at the finest spatial resolution are appropriately replaced by sinusoidal dipoles for which mutual impedances are available in closed-form analytical expressions. The fast wavelet bases transform is then exploited to effectively transfer the resultant matrix equation to multiresolution wavelet domain. Numerical results obtained by the compactly supported semi-orthogonal linear B-spline wavelet demonstrate dramatic reduction of the overall solution time without any degradation in the accuracy of the final solution

Efficient full-kernel evaluation for thin wire analysis

An accurate and fast approximation of the full cylindrical kernel in the thin-wire electric-field integral equation is proposed. The presented formulation is accurate for any ratio of the method of moments wire segment length Δ to the wire radius a, and anywhere in space, including on the wire surface. As a numerical example, the input impedance of a center-fed dipole is computed, showing convergence down to Δ/a = 10−4. A second numerical example shows the application of the model to a complicated geometry: a Koch fractal monopole antenna. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 477–480, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20672

Wavelet-like bases for thin-wire integral equations in electromagnetics

In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.

An advanced numerical model in solving thin-wire integral equations by using semi-orthogonal compactly supported spline wavelets

In this paper, the semi-orthogonal compactly supported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computationally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze electromagnetic transients in a lightning protection systems schematized as a thin-wire structure. The study is carried out in frequency domain; a discrete fast Fourier transform algorithm can be used to compute time profiles of the electromagnetic interesting quantities. The unknown longitudinal currents are expressed by using multiscale wavelet expansions. Thus, the thin-wire EFIE is converted into a matrix equation by the Galerkin method. Results for linear spline wavelets along with their comparison with conventional MoM that uses triangular basis functions and the point matching procedure are presented, for two case studies. Good agreement has been reached with a strong reduction of the computational complexity.

Wavelet-based efficient simulation of electromagnetic transients in a lightning protection system

In this paper, a wavelet-based efficient simulation of electromagnetic transients in a lightning protection systems (LPS) is presented. The analysis of electromagnetic transients is carried out by employing the thin-wire electric field integral equation in frequency domain. In order to easily handle the boundary conditions of the integral equation, semiorthogonal compactly supported spline wavelets, constructed for the bounded interval [0,1], have been taken into account in expanding the unknown longitudinal currents. The integral equation is then solved by means of the Galerkin method. As a preprocessing stage, a discrete wavelet transform is used in order to efficiently compress the Fourier spectrum of the waveform, used as the current source that directly strikes the LPS. Time profiles of electromagnetic quantities are then obtained by using an inverse discrete fast Fourier transform algorithm. The model has been validated by comparing the results with computed and measured data found in technical literature. A good agreement has been found with a significant computational reduction.

A simulation model for electromagnetic transients in lightning protection systems

This paper deals with the evaluation of electromagnetic transients in a lightning protection system (LPS). A field approach is used, based on the numerical solution of a modified version of the thin-wire electric field integral equation in the frequency domain. Time profiles of interesting electromagnetic quantities are computed by using a discrete fast Fourier transform algorithm. The model takes into account coupling effects among aerial parts and ground electrodes in order to correctly estimate the quantities which can determine electromagnetic hazard inside the LPS; transient touch and step voltages can be easily evaluated also taking into account the human body presence on the soil surface. To this purpose, a crucial point is the accurate evaluation of the current distribution among the earthed branches of the LPS and this needs to correctly consider mutual electromagnetic interference among the aerial parts and the earth-termination system of the same LPS. A suitable approach to consider the lossy soil is employed. Validation of the proposed model is performed by comparing the results with those measured and computed available in technical literature. Simulation examples related to realistic LPS structures are presented and discussed to show the flexibility and the accuracy of the model in the range of practical applications inside the volume to be protected.

Time-domain analysis of magnetic-coated wire antennas

The interaction of transient electromagnetic pulses (EMP) with perfect electric conductor thin wires with a thin magnetic coating, or mixed (dielectric and magnetic) coating, is studied in the time domain. The numerical procedure is based on the solution of the thin-wire electric field integral equation (EFIE) by the method of moments (MM), using a marching-on-in-time procedure. Numerical results are compared with measurements and with other authors' data. >

Time-domain integral equation methods for transient analysis

Some recent developments and extensions of the method of moments for analyzing, in the time domain, the interaction of transient electromagnetic waves with perfect electric conductors are described. The electric and magnetic time-domain integral equations (TDIEs) are formulated and their characteristics briefly discussed. Some issues involved in the formulation and solution of the thin-wire electric-field integral equation are examined. The solution of the magnetic- and electric-field integral equations for bodies modeled by patches is considered. The problem of the instabilities that appear in the solution of the TDIEs is addressed. The possibilities of using postprocessing of the time-domain data to visualize the history of electromagnetic phenomena are illustrated. >

An integro-differential equation technique for the time-domain analysis of thin-wire structures. II. Numerical results

Presented here are the numerical results from a computer solution of the time-dependent thin-wire electric-field integral equation described in Part I of this paper. Both radiation and scattering problems are considered. The present results are validated by their Fourier transform of the frequency domain, where they are compared with independently computed data. A space-time sampling criterion is derived for predicting the highest frequency to which the time-domain calculations are accurate and found to be in accord with the numerical results. The time domain results are also shown to provide informative insights into the radiation characteristics of specific structures. Recommendations for further work are also presented.

The RCS of a metal plate with a resonant slot

A numerical method based on the thin-wire electric field integral equation is used to calculate the radar cross section (RCS) of a wire grid with a resonant slot. The numerical results are in good agreement with experimental data for a wire grid, where the antiresonance is found to occur at a slightly lower frequency than a similarly slotted plate.