Electric Field Integral Equation Method Research Articles

Расчет двузеркальной антенны c учётом влияния опор строгим методом

Calculation of a double reflector Cassegrain antenna with taking into account of struts was performed by electric field integral equation method with unknown surface electric current and physical optics method with multiple reflections. For the same Cassegrain antenna with circular polarization we compared characteristics (gain, efficiency, side-lobes) at frequencies 1.7 GHz, 3.4 GHz and 5.1 GHz for the structure with struts (quadripod) and without struts. Calculation of antenna characteristics is performed for variable diameter of quadripod at main reflector at frequencies 1.7 GHz and 5.1 GHz. Calculation by rigorous method showed increase of side-lobes in the planes of struts and increase of the cross-polarization. With this in mind, the side-lobes in diagonal planes are approximately the same as in structure without struts. Comparison of gain reduction due to the struts is done, when calculated by rigorous method and aperture method.

Tridiagonal and Block Tridiagonal Computed Sparse Preconditioners for Large Electrodynamic Electric Field Integral Equation (EFIE) Solution

In this work, we propose simple and efficient tridiagonal computed sparse preconditioners for improving the condition number for large compressed electric field integral equation (EFIE) method of moment (MoM) matrix. The preconditioner computation is based on the triangle and block triangle interaction and filled tridiagonally. The computed preconditioner is highly sparse and retains the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${O(N)}$ </tex-math></inline-formula> complexity of computation and preconditioner matrix solution time. Numerical results show the efficiency and accuracy of the proposed preconditioner.

Electromagnetic telemetry simulation in vertical drillings

Electromagnetic (EM) telemetry is one of the key research subjects that has increased application in transmitting real-time data between the borehole and surface during drilling. There are several methods that can be used to model an EM telemetry system, including the method of moments (MoM) and the electric field integral equation method. We have developed a pulse basis function for the MoM, which assists in the analytical estimation of thin wire kernel integrations and avoids singular problems when simulating current distributions. The scattering field is solved using the current distribution. We examine the method using a simple example of vertical drilling. In the model, a vertically placed drill string is driven through a layered earth model. The drill string represents a long, thin wire antenna with a source located near the drill bit. The validity of the method is confirmed by comparing our results to the analytical solution in a half-space model as well as the current distributions along the drill string derived from the proposed method with those derived from a commercial finite-element solver, COMSOL-Multiphysics. Furthermore, the efficiency of this method is demonstrated by comparing its computational costs with those of COMSOL. The simulated EM telemetry in a known geologic setting is then compared with a field data example. These comparisons show that the proposed method is accurate and efficient. Moreover, we develop insights into how the parameters needed for calculations alter current distributions along the drill string and the signal received at the surface. The proposed method is therefore useful for obtaining the optimal design parameters for EM telemetry systems.

Joint Petrophysical and Structural Inversion of Electromagnetic and Seismic Data Based on Volume Integral Equation Method

A joint petrophysical and structural inversion method for electromagnetic (EM) and seismic data based on the volume integral equation (VIE) is proposed in this paper. In the forward EM problem, only the contrast of conductivity is solved by the electric field integral equation method. However, in the forward seismic problem, both the contrasts of velocity and mass density are solved by the combined field VIE method. Both forward solvers are accelerated by the fast Fourier transform. In the inversion problem, by using the petrophysical equations about the porosity and saturation and applying the chain rule, we fuse the EM and seismic data and construct the joint petrophysical inversion equations, which can be solved by the variational Born iteration method. Then, in order to further enhance the reconstructed results of the joint petrophysical inversion, we enforce the structural similarity constraint between porosity and water saturation and add the cross-gradient function to the joint petrophysical inversion cost function. Two typical geophysical models based on the remote sensing measurement are used to validate the proposed methods. One is the cross-well model, and the other is the marine surface exploration model. The advantage of the joint inversion compared with the separate inversion is evaluated based on the resolution and the data misfits of the reconstructed profiles as well as the antinoise ability.

Discontinuous Galerkin Method Using Laguerre Polynomials for Solving a Time-Domain Electric Field Integral Equation

A discontinuous Galerkin time-domain electric field integral equation method based on a marching-on-in-degree (MOD) scheme for simulating transient responses of perfect electric conductor objects is proposed in this letter. With the help of half-Rao–Wilton–Glisson spatial basis functions, we can simulate transient scattering responses of three-dimensional structures with either conformal or nonconformal meshes. The weighted Laguerre polynomials are chosen as temporal basis functions and implemented for the MOD scheme. Under such circumstances, the developed algorithm eliminates late-time instabilities and the limitation of Courant–Friedrichs–Lewy criteria. In addition, we adopt a fast-Fourier-transform-based blocking scheme to accelerate the temporal convolution of the MOD procedure. Some numerical examples are given to validate its stability and accuracy.

A Discontinuous Galerkin Augmented Electric Field Integral Equation for Multiscale Electromagnetic Scattering Problems

A discontinuous Galerkin (DG) augmented electric field integral equation method based on the domain decomposition is proposed in this paper for full-wave solution of multiscale targets. The conventional surface integral equation-based DG method allowing both conformal and nonconformal discretizations for multiscale structures suffers from low-frequency breakdown. By augmenting the DG-EFIE with current continuity equation, the proposed scheme can alleviate the low-frequency breakdown. In the augmented system, the electric field integral equation and the current continuity equation are discretized by using hybrid basis functions including Rao–Wilton–Glisson (RWG) and half RWG basis functions. Since the half RWG basis is not divergence conforming, line charge degrees of freedom on the adjoining edges are introduced in this paper. It is observed that the resulting linear system is well conditioned at low frequencies, which leads to a rapid convergence over wide frequency band. Numerical examples demonstrate the accuracy and efficiency of the augmented system.

Spatially Large-Domain and Temporally Entire-Domain Electric-Field Integral Equation Method of Moments for 3-D Scattering Analysis in Time Domain

A novel spatially large-domain and temporally entire-domain method of moments (MoM) is proposed for surface integral equation (SIE) modeling of 3-D conducting scatterers in the time domain (TD). The method uses higher order curved Lagrange interpolation-generalized quadrilateral geometrical elements, higher order spatial current expansions based on hierarchical divergence-conforming polynomial vector basis functions, and temporal current modeling by means of orthogonal weighted associated Laguerre basis functions. It implements full temporal and spatial Galerkin testing and marching-on-in-degree (MOD) scheme for an iterative solution of the final system of spatially and temporally discretized MoM-TD equations. Numerical examples demonstrate excellent accuracy, efficiency, convergence, and versatility of the new MoM-MOD method. The results also demonstrate very effective large-domain MoM-TD SIE models of scatterers using flat and curved patches of electrical sizes of up to about 1.7 wavelengths at the maximum frequency in the frequency spectrum of the pulse excitation, higher order current expansions of spatial orders from 2 to 8 in conjunction with entire-domain Laguerre temporal bases, and minimal numbers of unknowns.

Modeling Radiated Emissions Through Shielding Boxes Based on the Tangential Electrical Field Samplings Over Openings

The radiation from radiators such as PCBs inside an enclosed shielding box with ventilation slots is an important issue for electromagnetic compatibility or interference characterizations. In this paper, a two-step process is proposed based on the equivalence principle and the electric field integral equation method to complete the radiation prediction. The tangential electric fields over the slots on shielding boxes are first sampled to be the equivalent magnetic currents radiated from internal PCBs. In the second step, to avoid the computation of complex nonanalytical dyadic Green's functions when the field radiation is computed directly from the equivalent source, the surface current induced by the equivalent magnetic current is calculated by the method of moments. As a result, the total radiated emission is the superposition of both equivalent magnetic current source and induced current. To prove the validity and accuracy of the proposed approach, near-field and far-field radiations from PCBs in enclosed environments are benchmarked and compared with simulated references.

Improved Augmented Electric Field Integral Equation Method for Modeling Micro-Scale Structures

An improved augmented electric field integral equation method for modeling micro-scale structures is proposed in this article. The scaling property of the matrix systems of the original electric field integral equation method and the corresponding augmented electric field integral equation method are analyzed in detail. It is found that though the augmented electric field integral equation method works well for ordinary structures at very low frequencies, the matrix is ill conditioned for micro-scale structures with very dense mesh. Different balancing techniques are studied to alleviate this problem. A normalization factor is proposed to make the system stable for electrically small structures, especially for micro-scale structures working at several GHz. Numerical results are presented to demonstrate the accuracy and stability of this method.

Alternative AEFIE‐EFIE method for broadband CEM simulations

AbstractIt is well known that electric field integral equation (EFIE) has the low frequency breakdown problem due to the decoupling of electric and magnetic field. Augmented electric field integral equation (AEFIE) method overcomes the low frequency breakdown. However, its performance degrades with the increasing frequency. To obtain a unified method that works for both low and high frequencies, a novel method using the EFIE complement process inside AEFIE is proposed. Numerical results demonstrated that this alternative AEFIE‐EFIE method is able to extend integral equations to wide band applications. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:1737–1740, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26919

Electric field integral equation approach for accurate modeling of transmission loss properties and leakage phenomena in NRD-guide of arbitrary cross section

An electric field integral equation method has been developed for accurately modeling both transmission losses and leakage behaviors along nonradiative dielectric (NRD) guides of arbitrary cross-sectional shape and arbitrary inhomogeneous dielectric permittivity. The method is verified by comparing its modeling results with measured ones as well as with results obtained from a mode-matching method for bench-mark structures. The leakage properties of elliptical NRD guides and also the complete losses in trapezoidal NRD guides are studied in detail for the first time to demonstrate the advantages of the new method. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.

Improved Stable Scheme for the Time Domain Integral Equation Method

A novel technique for improving the stability of time domain electric field integral equation (TD-EFIE) method is presented. The method involving the introduction of a new class of temporal basis functions employs a modified form of TD-EFIE to generate stable transient responses from arbitrarily shaped conducting objects, which possesses the advantage of simplicity in implementation. Numerical examples are given to demonstrate the accuracy and the efficiency of the proposed method

Electromagnetic Scattering by Mixed Conductor-Dielectric Bodies of Arbitrary Shape

A volume-surface electric field integral equation method of moments formulation that makes use of rooftop basis functions defined over prism elements is presented. The new prism elements and their associated basis functions are designed to work either independently or in conjunction with basis functions previously defined over tetrahedral elements. Good agreement is found when comparing results obtained using the present formulation with analytical and experimental results

Frequency Selective Shielding Screen by the Use of Artificial Media

We calculated the shielding characteristic of a three-dimensional array of strip conductors by using the electric field integral equation method and its expansion to an array structure. From reflection coefficients, the effective permittivity of the array is calculated. The effective permittivity becomes negative in the frequency range above resonance, in which the electromagnetic waves travel through the material in an evanescent mode and the transmission coefficient becomes very small.

Analysis and design of bridged NRD-guide coupler for millimeter-wave applications

A new nonradiative-dielectric (NRD)-guide directional coupler using two NRD waveguides interconnected with a bridge is proposed and demonstrated. Propagation constants of the bridged NRD-guide couplers are investigated with an electric-field integral-equation method, and modeling results show that there is a maximum of coupling coefficient when the thickness of the bridge is made around 0.68 of the plate separation. In this case, the coupling length is reduced approximately 60% and the bandwidth under the tolerance limits of /spl plusmn/0.5 dB of deviation for 3-dB coupling is nearly doubled with reference to its conventional counterparts. The use of a bridge not only improves the mechanical stability, but also makes the coupler performance reproducible. Experimental prototypes are fabricated with two 90/spl deg/ elbow bends that are used for the arms and the bridge-connected coupler section is terminated at both ends by tapered half-circle sections. A calibration procedure is used to remove mismatch effects between the NRD-guide and the rectangular waveguide in the measured results. Advantages of the new coupler as a passive component are shown for millimeter-wave integrated circuits.

Smith-Purcell radiation from a charge moving above a finite-length grating

Smith-Purcell radiation (SPR), generated by an electron beam traveling above a grating, is characterized by a broad range of frequencies. The radiated wavelength depends on the angle of observation according to the SPR resonance relationship and the bandwidth is inversely proportional to the number of the grating grooves. A rigorous theoretical model of SPR from a three-dimensional bunch of relativistic electrons passing above a grating of finite length is presented by an electric-field integral equation method. The finite-length grating results are compared with the case of an infinitely long grating assumption in which periodic boundary conditions are rigorously applied and with a model based on the image-charge approximation. The SPR resonance relationship is the same in all three formalisms. Significant errors in the strength of the radiated energy are introduced by the two approximations. In particular, for gratings with less than $\ensuremath{\sim}20$ periods, the image-charge approximation and the infinitely long grating assumption result in an order of magnitude too high and too low radiated energy per groove, respectively, in the plane transverse to the grating groove lines. Numerical examples are calculated for an $\ensuremath{\sim}18\text{ }\text{ }\mathrm{MeV}$ bunch traveling above different finite-length gratings with a period of 2.5 mm.

Time- and frequency-domain models for Smith-Purcell radiation from a two-dimensional charge moving above a finite length grating

Smith-Purcell radiation (SPR), formed by an electron beam traveling above a grating, is a very promising source of coherent radiation from the THz to the optical regime. We present two theoretical calculations of the SPR from a two-dimensional bunch of relativistic electrons passing above a grating of finite length. The first calculation uses the finite-difference time-domain approach with the total-field/scattered-field procedure for fields incident on the grating. This calculation allows good physical insight into the radiation process and also allows arbitrary geometries to be treated. The second calculation uses an electric-field integral equation method. Good agreement is obtained between these two calculations. The results of these theoretical calculations are then compared with a theoretical formalism based on an infinite-length grating. The latter formalism allows periodic boundary conditions to be rigorously applied. For gratings with less than approximately 50 periods, a significant error in the strength of the radiated field is introduced by the infinite-grating approximation. It is shown that this error disappears asymptotically as the number of periods increases. The Wood-Rayleigh anomalies, predicted in the infinite-grating approximation, were not seen in our finite-grating calculations. The SPR resonance condition is the same in all three formalisms. Numerical examples are presented for an approximately 18 MeV, 50 nC/m, 200 microm bunch traveling 0.6 mm above a ten-period echelle grating having a 2.-mm periodicity.

Loop star basis functions and a robust preconditioner for EFIE scattering problems

An electric field integral equation (EFIE) formulation using the loop-star basis functions has been developed for modeling plane wave scattering from perfect conducting objects. A stability analysis at the DC limit shows that the use of the Rao-Wilton-Glisson (RWG) basis functions results in a singular matrix operator. However, the use of the loop-star basis functions results in a well-conditioned matrix. Moreover, a preconditioner constructed from a two-step process, based on near interactions and an incomplete factorization with a heuristic drop strategy, has been proposed in conjunction with the conjugate gradient method to solve the resulting matrix equation. The approach is shown to be effective for resolving both the low frequency instability and the bad conditioning of the EFIE method. The computational complexity of the proposed approach is shown to be O(N/sup 2/).

Efficient evaluation of reaction integrals in the EFIE analysis of planar layered structures with uniaxial anisotropy

This paper presents an efficient implementation of the electric-field integral-equation (EFIE) method to deal with planar anisotropic layered printed structures. A convenient treatment of the kernel of the integral equation gives rise to reaction integrals that only involve quasi-singularities and R/sup -1/-type singularities. When the well-known Rao-Wilton-Glisson triangular basis functions are used in conjunction with the Galerkin's method, closed-form expressions are found for the singular parts of the self-reaction integrals, as well as for the inner convolution integrals of the remaining singular/quasi-singular reaction integrals. Thus, the present procedure sets the EFIE method as a competitive alternative to other formulations.

Treatment of singularities and quasi-static terms in the EFIE analysis of planar structures

This paper reports on some mathematical and numerical details of the application of the electric field integral equation (EFIE) method to the analysis of planar structures printed on multilayered substrates. Closed-form expressions for singular and hypersingular terms of the transverse electric field Green's dyadic (TEFGD) are identified so that they can be explicitly extracted out before solving the EFIE. The problems due to the presence of the hypersingular contribution, usually argued to preclude the application of the EFIE to planar structures, are solved. In addition, a low-frequency expansion of the TEFGD corresponding to a single layer substrate is carried out to recognize nonsingular electrostatic-type contributions that can eventually become very important for computational purposes.