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In this work, we introduce new integral formulations based on the convolution quadrature method for the time-domain modeling of perfectly electrically conducting scatterers that overcome some of the most critical issues of the standard schemes based on the electric field integral equation (EFIE). The standard time-domain EFIE-based approaches typically yield matrices that become increasingly ill-conditioned as the time-step or the mesh discretization density increase and suffer from the well-known DC instability. This work presents solutions to these issues that are based both on new Calderón strategies and quasi-Helmholtz projectors regularizations. In addition, to ensure an efficient computation of the marching-on-in-time, the proposed schemes leverage properties of the Z-transform—involved in the convolution quadrature discretization scheme—when computing the stabilized operators. The two resulting formulations compare favorably with standard, well-established schemes. The properties and practical relevance of these new formulations will be showcased through relevant numerical examples that include canonical geometries and more complex structures.

Integral equation formulations are a competitive strategy in computational electromagnetics but, lamentably, are often plagued by ill-conditioning and by related numerical instabilities that can jeopardize their effectiveness in several real case scenarios. Luckily, however, it is possible to leverage effective preconditioning and regularization strategies that can cure a large majority of these problems. Not surprisingly, integral equation preconditioning is currently a quite active field of research. To give the reader a propositive overview of the state of the art, this paper will review and discuss the main advancements in the field of integral equation preconditioning in electromagnetics summarizing the strengths and weaknesses of each technique. The contribution will guide the reader through the choices of the right preconditioner for a given application scenario. This will be complemented by new analyses and discussions which will provide a further and more intuitive understanding of the ill-conditioning of the electric field (EFIE), magnetic field (MFIE), and combined field integral equation (CFIE) and of the associated remedies.

Eddy currents are central to several industrial applications and there is a strong need for their efficient modeling. Existing eddy current solution strategies are based on a quasi-static approximation of Maxwell's equations for lossy conducting objects and thus their applicability is restricted to low frequencies. On the other hand, available full-wave solvers such as the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equation become highly ill-conditioned and inaccurate in eddy current settings. This work presents a new well-conditioned and stable full-wave formulation which encompasses the simulation of eddy currents. Our method is built upon the PMCHWT equation and thus remains valid over the entire frequency range. Moreover, our scheme is also compatible with structures containing holes and handles (multiply connected geometries). The effectiveness of quasi-Helmholtz projectors is leveraged to obtain a versatile solver, which is computationally efficient and allows for a seamless transition between low and high frequencies. The stability and accuracy of the new method are demonstrated both theoretically and through numerical experiments on canonical and realistic structures.

Several recent contributions have envisioned the possibility of increasing currently exploitable maximum channel capacity of a free-space link, both at optical and radio frequencies, by using vortex waves, i.e., carrying orbital angular momentum (OAM). Our objective is to disprove these claims by showing that they are in contradiction with very fundamental properties of Maxwellian fields. We demonstrate that the degrees of freedom (DoFs) of the field cannot be increased by the helical phase structure of electromagnetic vortex waves beyond what can be done without invoking this property. We also show that the often-advocated over-quadratic power decay of OAM beams with distance does not play any fundamental role in the determination of the channel DoF.

A new regularization technique for graph Laplacians arising from triangular meshes of closed and open structures is presented. The new technique is based on the analysis of graph Laplacian spectrally equivalent operators in terms of Sobolev norms and on the appropriate selection of operators of opposite differential strength to achieve a multiplicative regularization. In addition, a new 3-D/2-D nested regularization strategy is presented to deal with open geometries. Numerical results show the advantages of the proposed regularization as well as its effectiveness when used in spectral partitioning applications.

Machine learning (ML) is the study of computational methods for improving performance by mechanizing the acquisition of knowledge from experience. As a modern data-driven optimization and applied regression methodology, ML aims to provide increasing levels of automation in the knowledge engineering process, replacing much time-consuming human activity with automatic techniques that improve accuracy and/or efficiency by discovering and exploiting regularities in training data. Indeed, many ML and data-driven methods, such as conventional artificial neural networks (ANNs), were introduced and studied within electromagnetics a few decades ago. However, these past studies did not benefit from the most recent advances in ML, which have been driven by the present confluence of improved hardware performance at lower cost, advanced network algorithms and architectures, data science, and considerable efforts dedicated to advancing the computational electromagnetics (CEM) benchmark. Today, a broader family of ML techniques based on ANNs has been developed. Examples include deep neural network (DNN), convolutional neural network (CNN), recurrent neural network, generative adversarial network, and deep reinforcement learning, which have been successfully applied to different engineering and science problems, ranging from image and video recognition, social media services, virtual personal assistant to autonomous vehicles, to name a few. This naturally suggests that applying ML to real-world electromagnetic problems could be one of the emerging trends in ML and artificial intelligence (AI) –. Indeed, ML has been becoming an important complement to existing experimental, computational, and theoretical aspects of electromagnetics. [ABSTRACT FROM AUTHOR]

An effective method for identifying inertia characteristics of cone-shaped space target based on deep learning is proposed. The inertia ratio is determined by the time-varying scattering fields from the cone-shaped targets. The multistatic method is introduced to reduce the evaluation time of time-varying scattering fields. The micro-Doppler spectrogram (MDS) dataset is constructed by the time–frequency analysis with numerical simulation method, point scattering model, and experimental tests. The compressed dataset is further achieved by truncated singular value decomposition (SVD). Finally, the micromotion parameter identification model is constructed to identify the inertia ratio for the cone-shaped space target. The interaction loss function and the feedforward denoising convolutional neural networks (DnCNNs) are employed to improve the identification accuracy. Parameters identification of the precession frequency, precession angle, spin frequency, and inertia ratio with both simulation and experiment datasets demonstrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following shortcomings: 1) ill-conditioning when the frequency is low; 2) ill-conditioning when the discretization density is high; 3) ill-conditioning when the structure contains global loops (which are computationally expensive to detect); 4) incorrect solution at low frequencies due to a loss of significant digits; and 5) the presence of spurious resonances. In this article, quasi-Helmholtz projectors are leveraged to obtain magnetic field integral equation (MFIE) that is immune to drawbacks 1)–4). Moreover, when this new MFIE is combined with a regularized electric field integral equation (EFIE), a new quasi-Helmholtz projector-combined field integral equation (CFIE) is obtained that also is immune to 5). The numerical results corroborate the theory and show the practical impact of the newly proposed formulations. [ABSTRACT FROM AUTHOR]

The time domain-electric field integral equation (TD-EFIE) and its differentiated version are widely used to simulate the transient scattering of a time dependent electromagnetic field by a perfect electric conductor (PEC). The time discretization of the TD-EFIE can be achieved by a space-time Galerkin approach or, as it is considered in this contribution, by a convolution quadrature using implicit Runge–Kutta methods. The solution is then computed using the marching-on-in-time (MOT) algorithm. The differentiated TD-EFIE has two problems: 1) the system matrix suffers from ill-conditioning when the time step increases (low frequency breakdown) and 2) it suffers from the DC instability, i.e., the formulation allows for the existence of spurious solenoidal currents that grow slowly in the solution. In this article, we show that 1) and 2) can be alleviated by leveraging quasi-Helmholtz projectors to separate the Helmholtz components of the induced current and rescale them independently. The efficacy of the approach is demonstrated by numerical examples including benchmarks and real-life applications. [ABSTRACT FROM AUTHOR]