Electric Field Integral Equation Research Articles

Breast tumor detection with TR‐DORT based on multilayered Green's function theory

AbstractUltrawideband (UWB) time‐reversal techniques are widely used in microwave imaging systems to detect and localize breast tumors. Measuring the scattering electromagnetic fields from a breast phantom can be time‐reversed and back‐propagated to refocus on a tumor. In this study, a Debye model was applied to the breast phantom. Using the decomposition of the time‐reversal operator (TR‐DORT), images were obtained in the UWB frequency range of 3.1–10.6 GHz. The conventional TR imaging method employs the free‐space Green's function to refocus on the tumor, which degrades refocusing in a lossy and dispersive breast phantom. We propose the use of the cylindrical dyadic Green's function in a three‐layer medium for TR imaging. The excitation system consists of a circular array of spiral antennas. The imaging results of the proposed Green's function in TR‐DORT were subsequently calculated, indicating successful tumor detection in different application scenarios of the lossy and dispersive breast phantom.

Manufactured solutions for an electromagnetic slot model

The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell's equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. We demonstrate the effectiveness of these approaches for a variety of cases.

Finite difference delay modelling for analysis of shielding effectiveness of perforated conductive enclosure

AbstractThis paper introduces finite difference delay modelling (FDDM) for computing the shielding effectiveness (SE) of a conductive enclosure with an aperture against electromagnetic pulses. FDDM offers optimal accuracy and stability for analysing complex structures. The time domain electric field integral equation (TD‐EFIE) for the conductive enclosure is derived by imposing boundary conditions on the perfect electrical conductor (PEC) surface in the Laplace domain. Time discretization is based on finite differences, and the Laplace‐to‐Z transform mapping is utilized. Fast Fourier Transform (FFT) is employed to expedite the FDDM solution process. Both frequency domain shielding effectiveness (FD‐SE) and time domain shielding effectiveness (TD‐SE) are evaluated using this approach. Finally, to validate the accuracy of the proposed method, results are compared with simulations using CST‐MWS software and the frequency domain moment method.

Powerful numerical method for analysis of electromagnetic scattering from multiple 3D coated targets buried under rough surface

ABSTRACT In this work, an efficient numerical method is proposed for three-dimensional (3D) electromagnetic scattering from multiple coated targets buried under a two-dimensional dielectric rough surface. In the proposed method, the interior region of each coated target is regarded as an independent subregion. The field within each coated target is modeled by 3D vector finite element method (FEM). The multiple scattering interactions between the buried targets and between targets and rough surface are considered by the electric field integral equation and the Poggio–Miller–Chang–Harrington–Wu integral equations, respectively. The fields inside and outside the targets are coupled together via boundary conditions on the boundary of each target. To improve the calculation efficiency and reduce the memory requirement, the fast multipole technique is used in our method. The presented method is numerically validated by comparing it with method of moments and conventional FEM-boundary integral method (BIM). The results indicate that, compared with traditional FEM-BIM, our method has significant advantages in computational efficiency and memory requirements.

Revealing the Invisible: Imaging Through Non-Radiating Subspace

This paper presents a novel modification to the subspace optimization method (SOM) for solving inverse scattering problems in diverse background media. By incorporating sequential quadratic programming (SQP), a fast and accurate optimization technique, our approach aims to improve the reconstruction of dielectric objects buried in complex environments. We investigate the influence of non-radiating (NR) subspace reconstruction on imaging quality by analyzing the induced current-exterior field mapping operator's singular values. The scattering formulation of direct problems is performed through numerical methods such as coupled dipole method, finite elements-boundary integral, and electric field integral equations. Radiating and non-radiating objective functions are defined and minimized using SQP to evaluate the effectiveness of the proposed method. Numerical experiments demonstrate significant enhancements in imaging quality, robustness, and computational efficiency compared to existing techniques. This modified SOM offers a promising avenue for precise and reliable reconstruction of electromagnetic scattering objects, with potential applications in various fields including medical imaging, remote sensing, and non-destructive evaluation.

Investigation of super-resolution in microsphere-assisted microscopy with the Poynting vector of the dipole model.

In this paper, the Fourier spectrum of an image in microsphere-assisted microscopy (MAM) and the wavenumber decomposition of the Poynting vector of the dipole model are compared for the first time to study the super-resolution performance within several wavelengths in MAM. Firstly, an experiment using microsphere-assisted microscopy is performed, and the fast Fourier transformation (FFT) spectra of the images along the distance are studied. Then the Poynting vector in the point dipole field is theoretically investigated based on the spectral decomposition of dyadic Green's function. Our study finds that the result of decomposition of the Poynting vector corresponds with the propagation results of components with different transverse wavenumbers kρ in an experiment. Even when kρ reaches 1.7k0, the waves can still arrive outside one wavelength. Our work is the first effort (to our knowledge) to associate the Fourier spectrum and the decomposition of the Poynting vector together, and it may contribute to the quantitative exploration of super-resolution performance in MAM in the future.

The free-space dyadic Green function is orthogonal to its curl

The free-space dyadic Green function in electromagnetics is orthogonal to its own curl on any spherical surface whose center is the source point.

Dipole-dipole interactions in the presence of a topological insulator stratified sphere: dyadic Green’s function method

Dyadic Green’s functions (DGFs) are developed for calculating electric fields induced by multiple sources in the presence of a topological insulator (TI) stratified sphere within the framework of axion electrodynamics. Generalizing our previous work, these sources can be placed at arbitrary locations rather than be limited outside the TI stratified sphere. Utilizing these DGFs, we explore the topological magneto-electric (TME) effect of the dipole–dipole interaction in the presence of composite structures of an alternating metal-TI stratified sphere, causing some modifications of the energy transfer (ET) enhancement spectrum. Furthermore, for the multipolar resonances of the metal shells, we find the TME-induced red-shifts of each bonding and antibonding mode in the ET enhancement spectrum are independent on the locations and orientations of the two dipoles but only depend on the configuration of these composite structures. These phenomenological findings provide some useful guidance with experimenters to design realistic experiments for exploring possible unique TME signatures via the energy transfer between molecules near/in TI multicoated nanoparticles in the near-infrared region.

Low-Frequency Stabilization for the B-Spline-Based Isogeometric Discretization of the Electric Field Integral Equation

Low-Frequency Stabilization for the B-Spline-Based Isogeometric Discretization of the Electric Field Integral Equation

Composite Scattering Study of Layered Rough Surface withTarget based on CCIA

In this paper, a fast Cross Coupling iterative Approach (CCIA) is proposed for studying the composite scattering of the layered rough surfaces with buried target, which uses forward backward method (FBM) to solve the electric field integral equations (EFIE) of the layered rough surface and bi-conjugate gradient method (BI-CG) to solve the EFIE of the target, and the interaction between the rough surface and the target is achieved by updating the excitation term. The algorithm is applied to calculate the composite scattering coefficients of the rough surface with a buried target, the results match with those of the traditional numerical algorithm MOM while the error can be reduced to 10−3 by 6 iterations, and the convergence speed and calculation accuracy meet the requirements. The composite scattering coefficients and Angular Correlation Function (ACF) amplitudes of layered rough surface and dielectric targets with different conditions are calculated, and the effects of various factors such as target size and burial depth on the composite scattering characteristics are discussed. It is found that the buried targets will have a great influence on the scattering characteristics, weakening or neglecting the coupling between them will lead to larger errors. Moreover, the results show that ACF can suppress scattering from rough surfaces well, making the scattering characteristics of the target more obvious, which is important for detecting underground targets.

Far-zone analytical expressions for electromagnetic waves produced by a uniform-current loop placed in a uniaxial dielectric-magnetic material

We investigate the radiation generated by a current loop situated within an unbounded uniaxial dielectric-magnetic material characterized by a uniform current distribution. We employ dyadic Green functions in the frequency domain to derive closed-form expressions for the far-field radiation. Our analytical findings distinguish between two scenarios: one in which the loop’s axis aligns parallel to the optic axis and another where it is perpendicular to the optic axis. In cases where the loop’s axis parallel’s the optic axis, only magnetically extraordinary wave is emitted as a consequence. However, when the loop’s axis is perpendicular to the optic axis, both electrically and magnetically extraordinary waves are emitted. Our results demonstrate a pronounced dependence of the radiation pattern on the loop’s size, as observed for various loop radii.

An IGFBM-SAA Fast Algorithm for Solving Electromagnetic Scattering from Layered Media Rough Surfaces

This article proposes a new fast solution algorithm (IGFBM-SAA), which combines the Improved Generalized Forward and Backward Method (IGFBM) with Spectral Acceleration Approach (SAA), which can effectively solve the electromagnetic scattering problem of layered rough surface. In this article, the electric field integral equations (EFIE) for layered rough surfaces is established, and the traditional forward and backward method (FBM) is introduced. Then, based on the traditional FBM algorithm, an Improved Generalized Forward and Backward Method is proposed and, by using the SAA technique in its iterative process, the computation of matrix-vector multiplication is accelerated, thus enabling rapid solution. In the algorithm validation, the same rough surface was calculated using the MoM, FBM, and IGFBM-SAA. The study found that when root mean square (RMS) heights are h1=h2=0.1λ, the convergence accuracy can reach τ=10−7 after 14 iterations. However, as the roughness increases to h1=h2=0.3λ and h1=h2=0.5λ, the convergence accuracy falling to τ=10−5 and τ=10−5, respectively. This indicates that it is necessary to adjust the integration parameters to improve the convergence accuracy. In addition, it was found that when the size of the rough surface is 25.6λ, the computational times for calculations are 91 s (IGFBM-SAA), 197 s (FBM), and 410 s (MoM), respectively. When the size of the rough surface increases to 51.2λ, the computational time differences become more significant, with 236 s, 756 s, and 2547 s being the respective values. This indicates that the proposed algorithm in this article has significant computational speed advantages when dealing with larger rough surfaces. Based on this algorithm, this article studied the electromagnetic scattering characteristics of layered rough surfaces with different parameters (RMS height, dielectric constant, and correlation length), and relevant research results can provide valuable references for areas such as radar target recognition and radar stealth technology, thereby enhancing the accuracy and reliability of radar detection as well as radar stealthperformance.

Solution of electromagnetic scattering field of adjacent transmission towers based on reciprocity theorem

Due to the large number of transmission towers being built, the dense distribution of transmission towers is inevitable in some areas. Densely distributed transmission towers will generate severe electromagnetic coupling, which will affect the setting of the passive interference protection distance between transmission towers and adjacent radio stations. Therefore, based on the traditional algorithm for solving the electromagnetic scattering field of a single electrically large target in wide area space, the electromagnetic coupling effect between multiple adjacent transmission towers within a range of 10 times the signal wavelength was considered. Based on the reciprocity relationship between the scattering electric field and the source and the introduced auxiliary field source as the intermediate variable, the electric field integral equation of the secondary scattering field generated by the electromagnetic coupling effect of adjacent transmission towers was derived, and the secondary scattering field is superimposed with the primary scattering field of the transmission generated by the electromagnetic wave excitation of the radio station, obtaining the electromagnetic scattering field at any point. In order to verify the accuracy of the algorithm proposed in this article, the scaled model experiments for the electromagnetic coupling effect between two transmission towers in an anechoic chamber were conducted. The average error of the algorithm proposed in this article is 6.73%, while the error of traditional algorithms is 20.18%. Compared with the traditional algorithm, the accuracy of the proposed algorithm is improved by 13.45%.

Research on Quasi-isotropic Radiation of Small Circular Arc Antenna

The radiation characteristics of circular arc antennas are studied by applying the method of moments (MoM) to solve the electric field integral equation (EFIE). Based on the triangular current distribution of small circular arc antennas, the analytical expression of radiation fields of circular arc antennas is derived. It is found that the circular arc antenna is equivalent to a superposition of an electric dipole and a magnetic dipole, resulting in near isotropic radiation pattern. Finally, both MoM and CST simulations show that the small arc antenna can realize the near isotropic radiation pattern.

Research on electromagnetic scattering characteristics of dipole clusters

AbstractThis paper equates chaff clouds to dipole clusters and studies the electromagnetic scattering problem of dipole clusters based on the linear method of moment (LMM) that solve the electric field Integral equation with the pulse basis function. Firstly, the radar cross section (RCS) of three dipole elements is calculated. The dipole element is divided into 11 segment line units using pulse basis functions. The actual chaff clouds are modeled as two nearest dipole cluster models, which are cubic dipole cluster with uniform distribution formed and spherical dipole cluster with Gaussian distribution formed. The total RCS and total E‐Field magnitude of two dipole cluster models were calculated. Finally, two physical models are constructed based on the simulation models and an experiment is designed. The electromagnetic scattering characteristics of the two models are measured, which verifies the accuracy of the simulation results and the operability of the experiment.

An efficient adaptive h‐refinement for the RWG‐based electric field integral equation applied to antennas with waveport

AbstractAn approximation scheme that combines approximate solutions with error estimators to accelerate the adaptive h‐refinement of the RWG‐based method of moments (MoM) with the electric field integral equation (EFIE) is presented. The scheme is effectively implemented by using the near‐field matrix to solve the approximate solution. Several conventional error estimators incorporated with the scheme are investigated. Compared to using the full MoM system, it significantly reduces the computational cost while maintaining the refinement effect. Numerical results indicate that the scheme could accelerate the adaptive refinement, yielding significant reductions in computational time and memory requirements.

A Low-Frequency Stable, Excitation Agnostic Discretization of the Right-Hand Side for the Electric Field Integral Equation on Multiply-Connected Geometries

In order to accurately compute scattered and radiated fields in the presence of arbitrary excitations, a low-frequency stable discretization of the right-hand side (RHS) of a quasi-Helmholtz preconditioned electric field integral equation (EFIE) on multiply-connected geometries is introduced, which avoids an ad-hoc extraction of the static contribution of the RHS when tested with solenoidal functions. To obtain an excitation agnostic approach, our approach generalizes a technique to multiply-connected geometries where the testing of the RHS with loop functions is replaced by a testing of the normal component of the magnetic field with a scalar function. To this end, we leverage orientable global loop functions that are formed by a chain of Rao-Wilton-Glisson (RWG) functions around the holes and handles of the geometry, for which we introduce cap surfaces that allow to uniquely define a suitable scalar function. We show that this approach works with open and closed, orientable and non-orientable geometries. The numerical results demonstrate the effectiveness of this approach.

Integral Equation Residuals for Error Estimation and Internal Resonance Detection

The performance of the four basic residual error estimators for perfectly conducting targets is evaluated in connection with the Rao-Wilton-Glisson method of moments numerical solutions of the electric field, magnetic field, and combined field integral equations. Results for 17 perfectly conducting test targets are used to evaluate the performance. Tangential-field residuals appear to be more reliable than normal-field residuals for assessing accuracy. Residual estimates are shown to be poor when used to assess an equation based on the same boundary condition as the residual. Residuals are sensitive to internal resonance modes associated with the complementary boundary condition and can be used to detect spurious solutions due to their presence.

Laplacian Filtered Loop-Star Decompositions and Quasi-Helmholtz Filters: Definitions, Analysis, and Efficient Algorithms

Quasi-Helmholtz decompositions are fundamental tools in integral equation modeling of electromagnetic problems because of their ability of rescaling solenoidal and non-solenoidal components of solutions, operator matrices, and radiated fields. These tools are however incapable, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">per se</i> , of modifying the refinement-dependent spectral behavior of the different operators and often need to be combined with other preconditioning strategies. This paper introduces the new concept of filtered quasi-Helmholtz decompositions proposing them in two incarnations: the filtered Loop-Star functions and the quasi-Helmholtz filters. Because they are capable of manipulating large parts of the operators’ spectra, new families of preconditioners and fast solvers can be derived from these new tools. A first application to the case of the frequency and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> -refinement preconditioning of the electric field integral equation is presented together with numerical results showing the practical effectiveness of the newly proposed decompositions.

Isogeometric Analysis of Electric Field Integral Equation on Multipatch NURBS Surfaces With Discontinuous Galerkin

Isogeometric Analysis of Electric Field Integral Equation on Multipatch NURBS Surfaces With Discontinuous Galerkin