Electromagnetic Problems Research Articles

A matrix‐free variant of the distorted Born iterative method for seismic full‐waveform inversion

AbstractThe distorted Born iterative method reduces a nonlinear inverse scattering problem to a sequence of (ill‐posed) linear inverse scattering problems that can be solved using a regularized least‐squares formulation. This method was originally applied to two‐dimensional electromagnetic problems but has been implemented to solve acoustic and electromagnetic problems in three dimensions. It has also been applied to seismic problems but only for moderately large two‐dimensional models. Previous applications of the distorted Born iterative method to seismic inverse scattering were based on a matrix representation of the relevant integral operators. The matrix‐based implementation is simple and transparent but not very suitable for large‐scale computations since the memory requirement and computational cost scales like N2 and N3, where N is the number of grid blocks. In this paper, we introduce a matrix‐free variant of the distorted Born iterative method, which is much more suitable for large‐scale problems, since the memory requirements and computational cost have been reduced to N and Nlog(N), respectively. Our matrix‐free implementation utilizes a fast‐Fourier‐transform‐accelerated iterative method to solve the linear system that results after discretization. In the computation of Fréchet derivatives, we avoid the direct computation of Green's functions for heterogeneous media, by solving an equivalent direct scattering problem. The adjoint of the Fréchet derivative operator is also computed in an efficient matrix‐free manner, by exploiting the physical interpretation and reciprocity of the Green's function. We illustrate the potential of the matrix‐free variant of the distorted Born iterative method using synthetic waveform data for large two‐ and three‐dimensional models. The main conclusion is that the distorted Born iterative method has been transformed into a more practical tool for seismic as well as electromagnetic and acoustic nonlinear inverse scattering.

The theory of scaling

Scaled experimentation is an important approach for the investigation of complex systems but for centuries has been impeded by the want of a scaling theory that can accommodate scale effects. The present definition of a scale effect is founded on the violation of an invariance principle arising out of dimensional analysis, i.e. dimensionless equations do not change with scale. However, apart from all but the most rudimentary of systems, most dimensionless governing equations invariably do change with scale, thus providing a very severe constraint on the reach of scaled experimentation. This paper introduces the theory of scaling that in principle applies to all physics and quantifies either implicitly or explicitly all scale dependencies. It is shown here how the route offered by dimensional analysis is nothing more than a particular similitude condition among a countable infinite number of alternative possibilities provided by the new theory. The theory of scaling is founded on a metaphysical concept where space is scaled and the mathematical consequences of this are reflected in the governing equations in transport form. The theory is trialled for known problems in continuum mechanics, electromagnetism and heat transfer to illustrate the breath of the approach and additionally demonstrate the advantages offered by additional forms of similitude.

GNSS Antenna Pattern Prediction and Placement Optimization: A Prototype Method Using Machine Learning to Aid Complex Electromagnetic Simulations Validated on a Vehicle Model

An antenna’s radiation pattern is dependent on its geometrical characteristics and its antenna’s surroundings, materials, and geometries. As such, to predict the antenna’s performance in complex environments, such as that of small antennas on large vehicles, it is necessary to obtain a model that represents such a full scenario, so that the simulation may be accomplished in the process of antenna design and placement. Due to the complex and electrically large nature of some electromagnetic problems, the detailed representation, even for a simplified model, may imply a large computational effort, both in terms of time and memory, is needed to perform the simulation. This paper evaluates how machine learning models can be used to mitigate the computational effort required to predict the behavior of antennas requiring complex modeling. It is proposed to start from a more simplified model of the electromagnetic structure to obtain a prediction for the correct solution, without needing to simulate the full structure in every iteration, and to combine this with prediction algorithms to obtain the solution of the full problem. The proposed solution uses convolutional neural networks (U-Net) of a certain accuracy to help with the correct placement of small antennas on autonomous vehicles. The standard approach requires the simulation of a full model at each test position, requiring high computational time and memory. With this new proposal, it is possible to analyze more positions and radiation patterns in a much shorter time, and with less memory, when compared with the solution from the full model. Along with this methodology for each simulation, a Bayesian optimizer is proposed to improve the search process for the best location, leading to a reduction in the required steps. This methodology was applied to support the correct positioning of a GNSS antenna with reference to a set of performance indicators required for autonomous vehicles, but it can be also applied to larger and more complex structures, allowing one to reduce the simulation time of a large electromagnetic structure and the search time for the optimum location.

Deposition of Thick SiO2 Coatings to Carbonyl Iron Microparticles for Thermal Stability and Microwave Performance.

Thick dielectric SiO2 shells on the surface of iron particles enhance the thermal and electrodynamic parameters of the iron. A technique to deposit thick, 500-nm, SiO2 shell to the surface of carbonyl iron (CI) particles was developed. The method consists of repeated deposition of SiO2 particles with air drying between iterations. This method allows to obtain thick dielectric shells up to 475 nm on individual CI particles. The paper shows that a thick SiO2 protective layer reduces the permittivity of the 'Fe-SiO2-paraffin' composite in accordance with the Maxwell Garnett medium theory. The protective shell increases the thermal stability of iron, when heated in air, by shifting the transition temperature to the higher oxide. The particle size, the thickness of the SiO2 shells, and the elemental analysis of the samples were studied using a scanning electron microscope. A coaxial waveguide and the Nicholson-Ross technique were used to measure microwave permeability and permittivity of the samples. A vibrating-sample magnetometer (VSM) was used to measure the magnetostatic data. A synchronous thermal analysis was applied to measure the thermal stability of the coated iron particles. The developed samples can be applied for electromagnetic compatibility problems, as well as the active material for various types of sensors.

Interaction effects from the elastodynamic scattering by two symmetric spherical cavities

The scattering of harmonic waves has been studied extensively for problems in quantum mechanics, acoustics, electromagnetics, and elasticity. Solutions to elastodynamic problems are the basis for ultrasonic non-destructive evaluation measurement models. Therefore, in this study, we investigate the use of the boundary element method (BEM) in the frequency domain using an off-boundary technique in which the observation points are taken inside the scattering object. This methodology removes both non-integrable singularities from the domain of integration along with avoiding ill-conditioning effects that occur at fictitious eigenfrequencies of which both require using special computationally demanding procedures to obtain solutions. Additionally, we employ both free and half-space fundamental solutions (Green’s displacement tensors) to investigate the elastodynamic scattering of an incident, plane, time-harmonic longitudinal wave in the frequency domain of a homogeneous, isotropic, and linear elastic solid with one or two spherical cavities. The half-space fundamental solution reduces the number of required boundary elements in half, which significantly reduces computational resource requirements. We only consider spherical cavities in this paper to illustrate the full and half-space off-boundary BEM and analyze the interaction effects associated with the elastodynamic scattering by two symmetric spherical cavities. To verify the validity of the free and half-space off-boundary BEM formulations, surface displacement results are compared with existing surface displacement results and show good agreement. Finally, the half-space off-boundary BEM is used to illustrate the interaction effects of the back and forward scattered displacement fields as a function of the distance from the spherical cavities.

An Efficient SSFEM-POD Scheme for Wideband Stochastic Analysis of Permittivity Variations

Stochastic analysis using polynomial chaos expansion (PCE)-based spectral stochastic finite-element method (SSFEM) is computationally expensive and is impacted by the curse of dimensionality. In this article, a low-dimensional basis is developed to approximate the problem using proper orthogonal decomposition (POD) to employ the PCE-based SSFEM, thereby resulting in an efficient intrusive formulation for uncertainty quantification (UQ) over a wide frequency band. Galerkin’s projection of vector finite elements for an electromagnetic (EM) problem with relative permittivity variations in multiple dielectric regions is formulated. The proposed method is shown to be computationally efficient and gives accurate results for a range of frequencies with single computation. It is also shown that this approach does not scale adversely with the number of stochastic parameters and has significantly lower memory requirement.

Fast and Numerically Stable Analytical Computations for the Power Induced in Cylindrical Multilayered Conductors Under External Magnetic Fields

Despite the spectacular development of numerical methods, the use of analytical formulas to solve electromagnetism problems in multilayered complex structures still remains attractive due to their much shorter computation time. One of the most essential computations is a calculation on the proximity effects observed in a wire that is immersed in an external harmonic electromagnetic field. The mathematical model of this problem is known and contains Bessel functions, which are numerically unstable for very low and high arguments. In this article, a novel numerically stable algorithm for the computation of proximity effects and power induced in a multilayered cylindrical structure is presented.

Full f and gyrokinetic particle simulations of Alfvén waves and energetic particle physics

In this work, we focus on the development of the particle-in-cell scheme and its application to the studies of Alfvén waves and energetic particle (EP) physics in tokamak plasmas. The and full f schemes are formulated on the same footing adopting mixed variables and the pullback scheme for electromagnetic problems. The TRIMEG-GKX code (Lu et al 2021 J. Comput. Phys. 440 110384) has been upgraded using cubic spline finite elements and full f and schemes. The toroidal Alfvén eigenmode (TAE) driven by EPs has been simulated for the International Tokamak Physics activity (ITPA)-TAE case featured by a small electron skin depth , which is a challenging parameter regime for electromagnetic simulations, especially for the full f model. The simulation results using the scheme are in good agreement with previous work. Excellent performance of the mixed variable/pullback scheme has been observed for both full f and schemes. Simulations with mixed full f EPs and electrons and thermal ions demonstrate the good features of this novel scheme in mitigating the noise level. The full f scheme is a natural choice for EP physics studies, which allows for large variations of EP profiles and distributions in velocity space, providing a powerful tool for kinetic studies using realistic experimental distributions related to intermittent and transient plasma activities.

Reconfigurable microwave photonic mixer for hybrid macro-micro cellular systems.

Microwave photonic mixing can realize the frequency conversion of microwave signals in the optical domain, breaking through the bandwidth bottleneck and electromagnetic interference problems of traditional microwave mixing methods. In the background of the hybrid macro-micro cellular system, a wideband, large dynamic range and reconfigurable microwave photonic mixer is proposed, theoretically analyzed and experimentally demonstrated in this paper. By adjusting the modulator bias voltages and matching the proper digital domain operations, a microwave photonic mixer with reconfigurable functions including single-ended dispersion immune mixing, I/Q frequency down-conversion, image rejection mixing, and double-balanced mixing are realized, respectively. Meanwhile, optimizing the electrical attenuator using convex optimization can suppress the third-order intermodulation distortion (IMD3), maximize the conversion gain, and finally improve the spur-free dynamic range (SFDR). Experimental results show that the proposed scheme can be operated with a frequency from 5 to 20 GHz, and the SFDR can achieve 118.3 dB·Hz4/5. Over the whole frequency range, I/Q frequency down-conversion can be well conducted with an amplitude imbalance below 0.7 dB and a phase imbalance below ±0.7°. After an I/Q imbalance compensation algorithm, the image rejection ratio of over 60 dB is produced. The power fading caused by fiber dispersion is also compensated successfully. For a vector signal with 16 quadrature amplitude modulation, the best error vector magnitude (EVM) reaches 3.4%.

Flexible quasi-2D inversion of time-domain AEM data, using a wavelet-based complexity measure

SUMMARYRegularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional scale-dependent wavelet-based ℓ1-regularization term to cure the ill-posedness of the airborne (time-domain) electromagnetic induction inverse problem. The regularization term is flexible, as it can recover blocky, smooth and tunable in-between inversion models, based on a suitable wavelet basis function. For each orientation, a different wavelet basis function can be used, introducing an additional relative regularization parameter. We propose a calibration method to determine (an educated initial guess for) this relative regularization parameter, which reduces the need to optimize for this parameter and, consequently, the overall computation time is under control. We apply our novel scheme to a time-domain airborne electromagnetic data set in Belgian saltwater intrusion context, but the scheme could equally apply to any other 2D or 3D geophysical inverse problem.

Optical singularity dynamics and spin-orbit interaction due to a normal-incident optical beam reflected at a plane dielectric interface

The degenerate case of normal incidence and reflection of an optical beam (both paraxial and nonparaxial) at a plane isotropic dielectric interface, which is azimuthally symmetric in terms of the momentum-spatial variation of Fresnel coefficients but not in terms of the fundamental polarization inhomogeneity of the incident field, requires in-depth analyses. In this paper, we use the reflection and transmission coefficient matrix formalism to derive an exact field expression of a normal-reflected diverging beam. The availability of the exact field information allows controlled variations of the system parameters, leading to significant dynamics of phase and polarization singularities hitherto unanticipated in the literature. We carry out a detailed exploration of these dynamics in our simulated system, and also verify them experimentally by using an appropriate setup. We then use Barnett's formalism to determine the associated orbital angular momentum (OAM) fluxes, leading to a subtle interpretation and mathematical characterization of spin-orbit interaction (SOI) in the system. Our paper thus represents a nontrivial unification of the most fundamental electromagnetic reflection and transmission problem at a plane dielectric interface and the emerging areas of optical singularity dynamics with their understanding in terms of OAM flux and SOI. The normal-incidence--retroreflection geometry being especially amenable to applications, these beam-field phenomena are anticipated to have applications in interface characterization, particle rotation and manipulation, and other nano-optical processes.

Quasi-Gradient Nonlinear Simplex Optimization Method in Electromagnetics

Particle swarm optimization (PSO), genetic algorithm (GA), and nonlinear simplex optimization method (SOM) are some of the most prominent gradient-free optimization algorithms in engineering. When it comes to a common group of electromagnetic optimization problems wherein less than 10 optimization parameters are present in the problem domain, SOM features faster convergence rate vs PSO and GA. Nevertheless, PSO and GA still outperform SOM by having more accuracy in finding the global minimum. To improve the accuracy of SOM in problems with few optimization parameters, a quasi-gradient (Q-G) search direction is added to the conventional algorithm. An extra decision is made by the proposed algorithm to move alongside the reflection or quasi-gradient direction during the error-reduction operations. This modification will improve the accuracy of SOM, which otherwise fails in the examples presented in this article, to levels similar to PSO and GA, while retaining approximately 33% faster convergence speed with relatively small number of parameters, and 20% faster convergence speed with larger number of optimization parameters. Following a standard benchmark test verification, the proposed algorithm successfully solves a suite of electromagnetic optimization problems. Representative examples include the optimization of absorber dimensions in an anechoic chamber, and estimation of the properties of an unknown embedded object by scattered microwave signals.

Solving Electromagnetic Inverse Problem Using Adaptive Gradient Descent Algorithm

The nonlinear conjugate gradient (NLCG) algorithm is one of the popular linearized methods used to solve the frequency-domain electromagnetic (EM) geophysical inverse problem. During NLCG iterations, the model gradient guides the searching direction while the line-search algorithm determines the step length of each iteration. Normally, the line search requires solving the corresponding forward problem a few times. Since line search is usually computationally inefficient, we introduce the adaptive gradient descent (AGD) algorithm to accelerate solving the frequency-domain EM inverse problem within the linearized framework. The AGD algorithm is a variant of the classical gradient descent method and has been well-developed and widely used in deep learning. Rather than the time-consuming line search, its core idea is to algebraically manipulate the cumulative gradients and updates of the model from previous iterations to estimate the model parameter variables at the current iteration. For the inversion of magnetotelluric (MT) data, we here designed and implemented a framework using the AGD algorithm combined with the cool-down scheme to tune the regularization parameter. To improve the convergence performance of the AGD algorithm [specifying to Adam and root-mean-square propagation (RMSProp)], we proposed a tolerance strategy which has been tested numerically. To optimize the global learning rate, we carried out some comparative trials in the proposed inversion framework. The inverted results of synthetic and real-world data showed that both the AGD algorithms (Adam and RMSProp) can recover comparable results and save more than a third of CPU time compared with the NLCG algorithm.

Conformable finite element method for conformable fractional partial differential equations

<abstract><p>The finite element (FE) method is a widely used numerical technique for approximating solutions to various problems in different fields such as thermal diffusion, mechanics of continuous media, electromagnetism and multi-physics problems. Recently, there has been growing interest among researchers in the application of fractional derivatives. In this paper, we present a generalization of the FE method known as the conformable finite element method, which is specifically designed to solve conformable fractional partial differential equations (CF-PDE). We introduce the basis functions that are used to approximate the solution of CF-PDE and provide error estimation techniques. Furthermore, we provide an illustrative example to demonstrate the effectiveness of the proposed method. This work serves as a starting point for tackling more complex problems involving fractional derivatives.</p></abstract>

In situ generated gas bubble-directed self-assembly of multifunctional MgO-based hybrid foams for highly efficient thermal conduction, microwave absorption, and self-cleaning.

Developing multifunctional materials with superior thermal conductivity and microwave absorption is an effective means to address the increasingly serious electromagnetic (EM) compatibility and heat dissipation problems in modern electron devices. Here, multifunctional MgO/Mg(OH)2/C, MgO/M/C (M = Co, Ni, Cu), and MgO/NOx/C (N = Fe, Mn) hybrid foams were synthesized using a facile one-step gas-bubble-assisted combustion method, and their texture, composition, and properties were regulated by tuning salt type and feeding ratio. Our results show that the MgO/Co/C foams have high thermal conductivity (3.40-4.09 W m-1 K-1) with a filler load of 20-50 wt% at the Co2+ molar content of φ = 70 mol% and excellent EM wave absorption (EABW = 11.44 GHz), with a thickness of 2.1 mm and a minimal reflection loss of -59.42 dB at φ = 90 mol%. The enhanced properties are ascribed to the construction of foams with 3D interconnected networks and the synergistic effect of magnetic Co, insulating MgO, and dielectric C, which provide a continuous pathway for electron/phonon relay transmission and magnetic/dielectric dual losses. Moreover, the MgO/Co/C foams possess strong mechanical/hydrophobicity performance, tunable magnetic properties, and electrical conductivity, and can be applied in self-cleaning, electromagnetic interference, and heat management. Overall, this study offers a novel understanding of preparing multifunctional heat conductive-EM wave absorptive foam materials in modern electronic devices.

Principal Component Analysis Accelerated the Iterative Convergence of the Characteristic Mode Basis Function Method for Analyzing Electromagnetic Scattering Problems

Principal Component Analysis Accelerated the Iterative Convergence of the Characteristic Mode Basis Function Method for Analyzing Electromagnetic Scattering Problems

Reflection and transmission of nanoresonators including bi-isotropic and metamaterial layers: opportunities to control and amplify chiral and nonreciprocal effects for nanophotonics applications

Electromagnetic waves reflected from and transmitted through the multilayer nanoresonators including the main layer made of a bi-isotropic material or metamaterial sandwiched between dielectric, epsilon-near-zero or metallic spacer layers have been analytically modeled. The numerical and graphical analysis, based on the exact solution of the electromagnetic boundary problem, confirms opportunities to use such nanoresonators as utracompact polarization converters. The proposed systems are characterized by wide ranges of parameters and significantly reduced (subwavelength) thicknesses. The spacer layers can provide modification, control, and amplification of chiral and nonreciprocal effects for the reflected and transmitted radiation. The concept can be realized for various geometries of dielectric, epsilon-near-zero, metallic, bi-isotropic, metamaterial layers and used to develop new ultrathin, large area, and relatively easy-to-manufacture polarization and other devices for nanophotonics.

Static Energy Meters and the Electrical Environment Comply to the Standards But are Not Compatible

The energy transition contributes to a more sustainable use of electricity. Consequently, the loads that are connected in the electricity grid change from conventional linear loads towards non-linear time-variant loads, which are usually more energy efficient. This has resulted in many conducted electromagnetic interference problems, of which the interference on static energy meters is an impactful case as it can result in higher energy bills for consumers. This issue occurs when highly pulsed loads are connected to the static energy meter. For example, coming from a commercial off-the-shelf water pump, where errors up to 2675% are found, or from switching multimedia equipment resulting in a power generation of more than 600 W without any power generating equipment connected. Therefore, this article compares the interference waveforms with the waveforms as included in the relevant directives and standards. It is found that the test standards only cover frequency domain test methods, while the interference waveforms are more wide-band. Furthermore, those test methods do not cover the wide variety of waveforms that occur in the residential environment were the static energy meter is placed in.

Hierarchical dandelion-like CoS2 hollow microspheres: self-assembly and controllable microwave absorption performance.

The emerging electromagnetic radiation and interference problems have promoted the rapid development of microwave absorption materials (MAMs). However, it remains a severe challenge to construct high-performance microwave absorption materials with broadband, lightweight and corrosion resistance within low filling contents. Herein, hierarchical dandelion-like CoS2 hollow microspheres were reasonably constructed via a solvothermal-hydrothermal etching-in situ vulcanization process. The structure morphology, composition and electromagnetic performance of all samples have been thoroughly tested. The research results demonstrated that the structure morphology of the prepared samples with a volume ratio of 1 : 1 between ethanol and H2O remained intact without serious damage. Notably, the as-obtained hierarchical dandelion-like CoS2 hollow microspheres (25 wt%) exhibited excellent microwave absorption capacity with a minimum reflection loss (RLmin) of -47.3 dB and the corresponding effective absorption bandwidth (EAB) of 8.4 GHz at 3.3 mm. Moreover, the broadest effective absorption bandwidth (EAB, RL < -10 dB) reached 9.0 GHz (9.0-18.0 GHz) at the matching thickness of 3.2 mm. The unparalleled multiple features including hierarchical hollow structure, tunable complex permittivity as well as the enhanced impedance matching endowed CoS2 great promise as high-performance microwave absorbers for solving the problem of electromagnetic pollution.

Improved Hybrid Real-Binary PSO Using Modified Learning and Restarting Methods for Planar Microwave Absorber Designs

This paper proposes an improved hybrid real-binary particle swarm optimization (IHPSO) using modified learning and restarting methods to address electromagnetic optimization problems involving both continuous and discrete decision variables. The modified learning approach aims to improve the exploration and exploitation capabilities of IHPSO. A restarting mechanism is employed to randomly reposition the swarm of particles to prevent them from being stuck in the local optimum, while still directing the search process with the global best. To demonstrate the performance of the IHPSO, 23 benchmark functions are tested, and the results are compared with those of other traditional algorithms. In both unimodal and multimodal functions, IHPSO outperforms the original hybrid real-binary PSO. Finally, the proposed algorithm is used to design planar microwave absorbers, a classic hybrid real-binary electromagnetic optimization problem.