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This paper proposes to model and forecast realized volatility (RV) using the fractional Ornstein–Uhlenbeck (fO–U) process with a general Hurst parameter, H . A two-stage method is introduced for estimating parameters in the fO–U process based on discrete-sampled observations. In the first stage, H is estimated based on the ratio of two second-order differences of observations from different frequencies. In the second stage, with the estimated H , the other parameters of the model are estimated by the method of moments. All estimators have closed-form expressions and are easy to implement. A large sample theory of the proposed estimators is derived. Extensive simulations show that the proposed estimators and the large-sample theory perform well in finite samples. We apply the model and the method to the logarithmic daily RV series of various financial assets. Our empirical findings suggest that H is much smaller than 1 / 2 , indicating that the RV series have rough sample paths, and that the mean reversion parameter takes a small positive number, indicating that the RV series are stationary but have slow mean reversion. The proposed model is compared with many alternative models, including the fractional Brownian motion, ARFIMA, and HAR, in forecasting RV and logarithmic RV.

A computationally simple bias correction for linear dynamic panel data models is proposed and its asymptotic properties are studied when the number of time periods is fixed or tends to infinity with the number of panel units. The approach can accommodate both fixed-effects and random-effects assumptions, heteroskedastic errors, as well as higher-order autoregressive models. Panel-corrected standard errors are proposed that allow for robust inference in dynamic models with cross-sectionally correlated errors. Monte Carlo experiments suggest that under the assumption of strictly exogenous regressors the bias-corrected method of moment estimator outperforms popular GMM estimators in terms of efficiency and correctly sized tests.

Metasurfaces have developed rapidly with the extraordinary electromagnetic properties in electromagnetic wave control in recent years. However, the conventional metasurfaces design based on the Method of Moments (MOM), Finite Element Method (FEM) and Finite Integration Technique (FIT) are still time-consuming and demand significant computation. In this paper, we proposed a polynomial regression of standardized K-nearest neighbor algorithm (PS-KNN). The trained model shows an excellent prediction ability, the means square error (MSE) of the forward model is only 3.463 × 10−6. We further report a reverse model based on forwarding prediction, which automatically constructs and optimizes the meta-atom by standardizing the electromagnetic properties (amplitude, phase, etc.) of the metasurface as the input of characteristic parameters. The MSE of the reverse model is 1.589 × 10−3. Finally, we cascade the two models, and predicted successfully eight meta-atoms by the closed-loop network and arrange them into a focused array. The results demonstrate the algorithm model avoids extensive modeling operations and numerical calculation and over 300 times faster than traditional electromagnetic simulation software. It offers a novel effective methodology to accelerate the on-demand design of complex metasurfaces and optical structures.

Fast analysis and wideband design using method of moments are proposed for a radiating subarray in a parallel-plate slot array antenna with perpendicular-corporate feed in this paper. Applying the method of moments and a genetic algorithm to the subarray design enables fast electromagnetic analysis and easy optimization for wideband performance. A comparison with the HFSS simulation proves the superior efficiency of designing by the proposed approach. The simulated bandwidth of reflection below -14 dB for the subarray gets up to 13.1% by a two-layer geometry in this paper, much improved from the 7.7% by a three-layer structure or the 11.4% by a four-layer structure using the conventional design method based on the HFSS simulation. The fabricated 16×16-slot array shows a measured bandwidth of 13.2% (58.7 – 67.0 GHz) with a reflection below -10 dB and a high antenna efficiency greater than 70% over a bandwidth of 11.2% (59.7 GHz – 66.8 GHz). At the design frequency of 61.5 GHz, a high measured gain of 32.9 dBi with antenna efficiency of 81.8% is demonstrated.

A novel miniature THz resonator consisting of a finite-length slotted graphene cylinder wrapped around an infinite circular dielectric rod is proposed. A full-wave 3D electromagnetic scattering model is built using the method of moments (MoM) solution of the electric-field integral equation (EFIE) in the spectral domain. In order to gain better understanding of the associated physical effects, the obtained results are compared with a 2D model where the slotted graphene cylinder is assumed infinite. A good agreement between the 3D and 2D models if found. The dependence of the backscattering radar cross-section on the frequency is analyzed. It is found that in both cases this scatterer displays quasi-static Helmholtz resonance response in the sub-THz frequency range, a behavior previously known for perfectly electrically conducting (PEC) slotted cylinders. For both models, in-resonance surface current distributions and far-zone radiation patterns are given. The most important innovation is that due to the use of graphene the Helmholtz-mode resonance becomes electrically tunable.

A two-way parabolic equation (2W-PE) method based on machine learning is proposed to predict the spatial field strength of radio waves propagating over undulating terrain. The method first performs longitudinal domain decomposition on a step distance, and uses different algorithms to solve the 2W-PE in each subdomain. Then a simple obstacle model (SOM) containing three stepping units of different heights is introduced. A variety of undulating terrains can be approximated using the overlay combinations and lateral extensions of multiple SOMs, and combined with machine learning method, the boundary condition coefficients in different environments can be determined. The simulation results show that the proposed 2W-PE method is in good agreement with the method of moments (MoM), which verifies its accuracy and superiority.

Objective: The inverse problem of computing conductivity distributions in 2D and 3D objects interrogated by low frequency electrical signals, which is called Electrical Impedance Tomography (EIT), is treated using a Method-of-Moment technique. Methods: A Point-Matching-Method-of-Moment technique is used to formulate a global integral equation solver. Radial Basis Functions are adopted to express the conductivity distribution. Single-step quadratic-norm (L2) and iterative total variation (L1) regularization techniques are exploited to solve the inverse problem. Results: Simulation and experimental tests on a circular reconstruction domain show satisfactory performance in deriving conductivity distribution, achieving a Correlation Coefficient (CC) up to 0:863 for 70 dB voltage SNR and 0:842 for 40 dB voltage SNR. The proposed methodology with L2-norm regularization provided better results than traditional iterative Gauss-Newtons approach, whereas with L1-norm regularization it showed promising performance. Moreover, 3D reconstructions on a cylindrical cavity demonstrated superior results near the electrodes planes compared to those of the conventional linearized approach. Finally, application to EIT medical data for dynamic lung imaging successfully revealed the breath-cycle conductivity changes. Conclusion: The results show that the proposed method can be effective for both 2D and 3D EIT and applicable to many applications. Significance: Strong conductivity variations are successfully tackled with a very good Correlation Coefficient. In contrast to conventional EIT solutions based on weak-form and linearization on small conductivity changes, the proposed method requires only one step to converge with L2-norm regularization. The proposed method with L1-norm regularization also achieves good reconstruction quality with a low number of iterations.

International audience; In this paper, we present an efficient numerical method to calculate the frequency and time responses of the field scattered by an object buried between two random rough surfaces for a 2-D problem. This method is called Generalized PILE (GPILE) method because it extends the PILE method which considers only two surfaces or an object buried under a surface. The GPILE method solves the Maxwell equations rigourously by using a simple matrix formulation. The obtained results have a straightforward physical interpretation and allow us to investigate the influence of the object buried between the two rough surfaces. We distinguish the primary echo of the upper surface, the multiple echoes coming from the lower surface, and those arising from the object. The GPILE method is applied to simulate the Ground Penetrating Radar (GPR) signal at nadir. The resulting time response helps the user to detect the presence of the object buried between the two random rough surfaces.

A decomposition and reconstruction theorem (DRT) is introduced to advance computation and provide physical understanding for the scattering from fractal surfaces (FPs). The profile of FP is decomposed into test profiles (TPs), and the scattering of FP is reconstructed using the scattering of TPs to enhance the computational efficiency. A new method that applies DRT on the extended boundary condition method combined with the truncated singular value decomposition technique (TEBCM) is presented and referred to as TEBCM-DRT. The method of TEBCM-DRT is employed to solve the scattering from realistic soil surfaces, and the results are validated against other scattering models. Moreover, the efficiency of TEBCM-DRT and its validity range are investigated. The result shows that TEBCM-DRT improves computational efficiency to 1.95 x 10⁵ and 7.35 x 10² times, respectively, compared to TEBCM and the conventional method of moments for a wide range of roughness. In addition, TEBCM-DRT indicates that the amplitude and direction of propagation of scattering modes are dependent on deterministic TPs. This relationship benefits for obtaining the accurate height of an arbitrary point on the profile from bistatic scattering coefficients.

Electrostatic film actuators represent a promising new approach to drive a soft robot, but they lack a comprehensive model to link the design parameters and actuation performance, making actuator design and parameter optimization challenging. To solve this problem, we build a mathematical model based on the method of moments by assuming that each electrode consists of a large number of line charges. This model can directly deduce fluctuation in thrust and adhesive forces during actuator movement, as well as the distribution of electric potential and field strength, for analysis and optimization. It consumes shorter computing time and fewer computing resources, but with comparable accuracy, in comparison with previous indirect means. It is validated by results from both previous studies and on-site experiments. Based on this model, we generate numerous values of actuator output force for different structural parameters. By analyzing the tendency, we summarize a parameter optimization workflow and write an open-sourced program as an example to facilitate the parameter selection for actuator design starting from scratch.

A new architecture is provided for the efficient generation of shaped beams and multiple shaped beams (in amplitude, phase, and polarization), with leaky-wave (LW) metasurfaces (MTSs). Those antennas are usually fed by a surface-wave (SW) launcher, which evenly illuminates the MTS versus azimuth, through a cylindrical SW. When the interest lies in generating pencil beams or particular types of shaped beams, the required radiating aperture field (linked to the Fourier transform of the desired radiation pattern) on the MTS is almost azimuthally symmetric in amplitude. However, for a wide class of shaped beams, the desired aperture field is far from being azimuthally symmetric. This leads to an MTS design in which some sectors exhibit a very small surface impedance modulation. Those sectors tend to leave the SW intact until it reaches the rim of the surface, where the power is either reflected or diffracted at the slab rim. We solve this efficiency problem by reducing the amount of power fed into some sectors, through the use of an array of feeding monopoles. The azimuthal illumination of the feeder should be designed to match the azimuthal asymmetry of the desired aperture field. The corresponding MTS surface impedance is then determined using a method of moments (MoM)-based synthesis technique. Several examples are provided to illustrate the concept. The improvement in terms of antenna efficiency is numerically demonstrated.

Traveling-wave modulation is a form of space-time modulation which has been shown to enable unique electromagnetic phenomena such as non-reciprocity, beam-steering, frequency conversion, and amplification. In practice, traveling-wave modulation is achieved by applying a staggered time-modulation signal to a spatially-discrete array of unit cells. Therefore, the capability to accurately simulate spatially-discrete traveling-wave modulated structures is critical to design. However, simulating these structures is challenging due to the complex space-time dependence of the constituent unit cells. In this paper, a field relation (referred to as the interpath relation) is derived for spatially-discrete traveling-wave modulated structures. The interpath relation reveals that the field within a single time-modulated unit cell (rather than an entire spatial period) is sufficient to determine the field solution throughout space. It will be shown that the interpath relation can be incorporated into existing periodic method of moments solvers simply by modifying the source basis functions. As a result, the computational domain is reduced from an entire spatial period to a single time-modulated unit cell, dramatically reducing the number of unknowns. In the context of traveling-wave modulation, this enables researchers to efficiently simulate both complex structures with patterned unit cells in addition to continuous structures with infinitesimal unit cells., 15 pages

High-precision calculation of electromagnetic scattering plays an important role in industrial field. This study aims to apply the latest research results based on semi-analytical boundary collocation method to calculate computational electromagnetics. The article focuses on discussing some common mechanical bottlenecks encountered by semi-analytical boundary collocation method in simulating electromagnetic scattering, such as the non-uniqueness at internal resonance, the singularity and near singularity of the fundamental solution and the preconditioning problem. The article constructs a regularized method of moments based on the Burton-Miller formulation to avoid the non-uniqueness at internal resonance. The origin intensity factor and nearly singular factor are used to replace the singular and nearly singular terms of the interpolation matrix. A novel fast near-field approximation preconditioner is introduced to greatly reduce the number of iterations without significantly increasing storage and computational complexity. Numerical experiment shows that the Burton-Miller type regularized method of moments can accurately calculate radar cross section scattered by the NASA almond model and real human head.

An adaptive multilevel non-uniform grid (MLNG) algorithm is developed for the accelerated computation of fields radiated through composite metallic-dielectric radomes as well as antenna-radome interactions. The MLNG approach is applied to the mixed potential formulation of the coupled surface and volume electric field integral equations. The radome is decomposed into a hierarchy of subdomains (SDs) by an adaptive algorithm that closely follows the radome geometry, allowing significant savings in memory and CPU time. In the MLNG algorithm, only local generalized impedance matrices of the finest level SDs are evaluated. Far-zone potentials and fields are indirectly evaluated through a multilevel aggregation involving phase and amplitude compensated interpolation on non-uniform grids (NGs), requiring considerably fewer calculations as compared with the classical Method of Moments (MoM). The MLNG algorithm is incorporated in a preconditioned iterative solver. Accuracy as well as memory consumption and computation times of the algorithm are studied on realistic examples. The radome effect on the antenna input impedance and electric current density distribution is demonstrated. The method is validated by comparison with a commercial MoM software and shown to exhibit a computational complexity (CC) of O(NlogN), N being the number of unknowns.

To further improve the computational efficiency of the existing wave equation-based discontinuous Galerkin time-domain (DGTD) method for modeling electrically small structures, the weighted Laguerre polynomials are incorporated to span the fields in the temporal domain, which finally results in a set of recursive linear equations related to the Laguerre polynomials to be solved. Compared with conventional time integration methods, the proposed approach requires much fewer iterations and thus shows considerable improvement in terms of computational efficiency. With respect to the first-order Maxwell’s curl equation-based DGTD method with weighted Laguerre polynomials, the proposed method reduces the unknowns by more than a half and gives a lighter linear system for solution. In addition, block iterative solvers and the block lower-diagonal-upper (LDU) direct solver can be applied to facilitating the solution at the subdomain level. Three numerical examples are included to demonstrate the accuracy and efficiency of the proposed method. With the weighted Laguerre polynomials, the wave equation-based DGTD method is expected to be more efficient for electrically small structure modeling.

A novel time-domain (TD) integral-equation (IE) technique for analyzing the pulsed electromagnetic (EM) scattering by a 2-D metasurface, represented by a thin highly contrasting screen with combined dielectric and magnetic properties, is presented. The problem under consideration is formulated with the aid of the EM reciprocity theorem of the time-convolution time. Subsequently, upon discretizing the space–time solution domain, the reciprocity relation is cast into two independent matrix forms whose elements are derived analytically using the classic Cagniard–DeHoop (CdH) technique. The thus obtained convolution-type systems of equations are solved for induced electric and magnetic currents through a stable step-by-step updating procedure. The presented numerical method is finally validated using alternative TD solutions.

In this paper, a size-biased Poisson-Gamma Lindley distribution (SBPGLD) has been obtained by size-biasing the Poisson-Gamma Lindley distribution (PGLD) introduced recently by Nedjar and Zeghdoudi (2020). Some of its statistical properties have been discussed. The method of maximum likelihood and the method of moments for the estimation of its parameters have been discussed. Also, an application on the real data of survival times of (56) Indian state of Kerala individus infected with Nipah virus is given.

The method based on the partitioned inverse matrix formula and the Sherman–Morrison–Woodbury formula has been developed to solve the partial modification problems efficiently. However, it requires the meshes of the mother-structure, the add-structure, and the subtract-structure are separated or conformal. It is inconvenient and inflexible for users. In this letter, the integral equation discontinuous Galerkin (IEDG) with a mesh modification algorithm (MMA) is proposed to mitigate this problem. With the help of the IEDG and the MMA, the mother-structure and the add-structure can be meshed independently, and the mesh errors caused by removing the subtract-structure from the mother-structure are reduced. Numerical results are given to demonstrate the advantages of the improved method.

Surface differential equations (SDEs) are derived for the induced current on the outer surface of a perfectly electrically conducting (PEC) object for the first time. The derived equations are wave equations that describe the propagation of surface current waves along a PEC surface. A numerical method based on SDEs is proposed, which is named the eigenmode theory in this article. In this method, SDEs are discretized into a generalized eigenvalue equation, which can be used to obtain a series of modal currents and expand the surface current induced by any excitation. The modal currents are only dependent on the shape and size of the PEC object and are independent of any specific excitation, including frequency, feeding location, and so on. This property results in an eigenmode theory with great potential in many challenging antenna designs. Numerical examples for both scattering and radiation analyses demonstrate the effectiveness and accuracy of eigenmode theory and, thus, give evidence for the correctness of SDEs.

Lataa OA, kun julkaistu. This article studies the use of quality factor Q as a tool to design multiport antenna structures with matching networks. Approximative formulas for computing the Q -factor from the port impedances of multiport antennas are presented. We show that the achievable performance level can be reliably estimated based on the Q -factor without the need for computationally heavy and time-consuming matching network optimization. The efficiency of the proposed method is confirmed with a practical two-port antenna cluster design for smartphones operating in the 0.7-1.0 GHz frequency band. The results show that the proposed port impedance-based Q -factor formulas provide an efficient tool to accelerate the design process of multiport antennas.

This article proposes an efficient full-wave method to analyze the radiation pattern of an antenna in the presence of a multilayer axisymmetric radome. In this method, first, the field distribution on the antenna aperture is replaced with the respective equivalent currents to compute the incident electromagnetic field on the inner surface of the radome. The radome is then modeled with a cascaded network of two-port devices and generalized transmission lines based on the theory of surface equivalence and the method of moments. The cascaded network is used to relate the tangential components of the electromagnetic field at the inner surface of the radome to their counterparts at the outer surface of the radome which, in turn, are used to obtain the respective equivalent currents. Finally, these currents are used to determine the radiation pattern of the antenna in the presence of the radome. The efficiency of the proposed method is demonstrated by comparing the simulation results of several case studies with those obtained by the rival theoretical models in the literature or computed by commercial numerical codes.

Convergence studies of the Method of Moments solution of thin wires have long been handicapped by the issue of conditional convergence: when the segment length approaches the wire radius, the approximations typically made result in exponentially diverging solutions. In this communication, it is shown that it is the approximation of the singularity which is the main cause of this problem. Using the mixed potential integral equation, paralleling the classic RWG formulation for surfaces, the formulation in this communication approximates the surface (as opposed to equivalent filamentary) current, and applies Galerkin testing on the wire surface. The use of contemporary singularity-canceling integral transforms for highly efficient and accurate quadrature is demonstrated. Results are presented for typical thin-wire dipoles for both radiation and scattering problems. It is shown that with a rigorous treatment of the singularity, a far more comprehensive convergence study may be undertaken than previously demonstrated. Furthermore, the results shown justify the many years of successful use in practice of simple source models with modest mesh requirements.

We introduce a class of semiparametric time series models (SemiParTS) driven by a latent factor process. The proposed SemiParTS class is flexible because, given the latent process, only the conditional mean and variance of the time series are specified. These are the primary features of SemiParTS: (i) no parametric form is assumed for the conditional distribution of the time series given the latent process; (ii) it is suitable for a wide range of data: non-negative, count, bounded, binary, and real-valued time series; (iii) it does not constrain the dispersion parameter to be known. The quasi-likelihood inference is employed in order to estimate the parameters in the mean function. Here, we derive explicit expressions for the marginal moments and for the autocorrelation function of the time series process so that a method of moments can be employed to estimate the dispersion parameter and also the parameters related to the latent process. Simulated results that aim to check the proposed estimation procedure are presented. Forecasting procedures are proposed and evaluated in simulated and real data. Analyses of the number of admissions in a hospital due to asthma and a total insolation time series illustrate the potential for practical situations that involve the proposed models.

The method of moments has been widely used for estimating the parameters of a distribution. Usually lower order moments are wont to find the parameter estimates as they're known to possess less sampling variability. The method of moments may be a technique for estimating the parameters of a statistical model. It works by finding values of the parameters that end in a match between the sample moments and therefore the population moments (as implied by the model). the Method of moment Estimator is used to find out Estimates the parameters of PERT Distribution. We also compare equispaced and unequispaced Optimally Constructed Grouped data by the method of an Asymptotically Relative Efficiency. We also computed Average Estimate (AE), Variance (VAR), Standard Deviation (STD), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Simulated Error (SE) and Relative Absolute Bias (RAB) for both the parameters under grouped sample supported 1000 simulations to assess the performance of the estimators. Keywords: Method of Moments, PERT Distribution, equispaced and unequipped Optimal Grouped sample

In this communication, a paralleled interior penalty discontinuous Galerkin time-domain method based on the vector wave equation (IPDG-WE) combining with a generalized dispersive material (GDM) model is introduced. In addition, the auxiliary differential equation (ADE) technique is employed to establish a universal solution for scattering analysis of dispersive structures in a wide frequency range. The proposed method presents great characteristics of energy conservation and the optimal convergence rate even in low-order bases and exhibits promising competitiveness in CPU time and memory usage compared with the traditional Maxwell’s equations-based discontinuous Galerkin time-domain (DGTD-ME) method. Numerical simulations are executed to demonstrate the accuracy and efficiency of the proposed method, which realize twice the memory and triple the CPU time reductions.

We present a new approach for the analysis and design of radome structures. It makes use of extended domain macro-basis functions obtained from the characteristic basis function method in order to represent the current distribution over the radome. This involves computational advantages due to the reduction in the number of unknowns compared to conventional approaches. This approach involves dividing the scenario into two domains, antenna and radome, and calculating the influence between them using a technique that iteratively corrects the error of the currents on each domain. This technique can be used to analyze arbitrary-shaped radome antennas including several material layers with different thicknesses and dielectric properties that can embed frequency selective surfaces on any interface. Several test cases are presented for the validation of the proposed technique.

The characteristic mode (CM) approach has been applied to analyze the periodic and quasi-periodic structures efficiently. In this communication, an acceleration technique of the multilevel fast multipole algorithm (MLFMA) and a parallel scheme for the CM approach have been proposed to handle large-scale finite periodic and quasi-periodic structures in free space. The CM serves as a kind of entire-domain basis function to reduce unknowns in the method of moments (MoM). The MLFMA is used to accelerate the matrix-vector products (MVPs) between impedance matrix and eigenvectors, while the parallel technique is to reduce the time of generating a reduced matrix. The numerical examples have shown that, whether it is a connected structure or a nonconnected structure, the proposed method has good accuracy and efficiency.

The wideband scattering by the large-scale electrically connected finite periodic arrays is analyzed using the modified accurate subentire-domain (ASED) basis function method and the improved frequency-independent reaction (FIR). The size of matrix equation based on the modified ASED basis functions is less than that based on the elementary basis functions. Generation of the impedance matrices is still very time consuming in this method. To reduce generation time, the improved FIR is applied. In this technique, the matrix element is approximated as the form consisting of geometrical terms that are computed in advance and reused during frequency sweep. Several numerical examples of wideband analyses are performed. Simulation results validate the accuracy and efficiency of the proposed technique.

The time-domain electric current response of a transmission line located over a conducting thin layer is analyzed numerically with the aid of the Cagniard–DeHoop method of moments. Numerical examples validating the proposed computational methodology is presented.

A new model-based parameter estimation (MBPE) method for multilayer periodic EM surfaces is discussed in this article. By applying the proposed method to predict the generalized scattering matrix (GSM) of each unit layer section, the response of a composite structure can be determined by cascading GSMs while allowing the salient behavior of each section to be accurately captured. Based on the spectral properties of Green’s functions with high-order wavenumbers and chosen basis functions, an advanced interpolation model is developed to estimate the broadband response of periodic structures in a robust and efficient manner. It needs fewer samples in the interpolation compared to the state of the art, and no restriction for the sample selection is required. Numerical analysis has been carried out for two types of multilayer structures, and a good agreement between the conventional periodic method of moments (PMM) and the proposed method has been obtained.

For spaceborne transmitting systems, strip antennas provide a new scheme in boosting the radiation efficiency due to their availability in generating larger current moments. In this article, we investigate the theory of a very-low-frequency (VLF: 3–30 kHz) strip antenna immersed in a homogeneous anisotropic plasma. The focus lies on the analytical method for calculating the current distribution and input impedance of the antenna, where the current distribution, in this case, consists of two parts of distribution in both longitudinal and transverse directions. Kernel function for a strip antenna at arbitrary orientations is derived with the help of coordinate transformation, and the current integral equation is solved via the method of moments (MoM). Computations show that the surface currents on a strip antenna will concentrate near the edges of the strip, and the input impedance of the antenna will increase with either the length-to-width ratio or the dip angle. Simulation results using commercial software FEKO exhibit good consistency with the computed results, thus verifying the accuracy of the proposed method. By comparison of the input impedances with linear antennas, it is found that strip antennas are more efficient than linear antennas when the length-to-width ratio is selected properly.

This communication presents a formulation of the spectral-domain Method of Moments (spectral MoM) for the analysis of periodic multilayered structures with a number of metallized interfaces alternating patches and apertures. Edge singularity entire-domain basis functions are used to model the electric currents on the patches and the tangential electric fields in the apertures. The formulation is especially suitable to characterize high-order bandpass frequency selective surfaces (FSSs) made up of nonresonant elements. Also in this communication, the nonuniform fast Fourier transform (NUFFT) is used in the spectral MoM to cover the case of unit cells in skewed grids, which enables the analysis of nonrectangular periodic lattices with tightly packed elements. Numerical examples of the design of third-order and fifth-order bandpass FSSs are presented. The FSSs are made up of hexagonal patches and apertures arranged in an equilateral triangular lattice. Results are cross-checked against commercial software CST Microwave Studio (CST MWS), and excellent agreement is found, our in-house software being more than one order of magnitude faster than CST MWS. This CPU time saving makes the proposed formulation very convenient for full-wave optimization and design.

A numerically robust and computationally efficient approach for evaluating a planar layered substrate’s static Green’s function is developed based on the adaptive form of the spectral differential equation approximation method. The method uses a $p$ th-order finite element method (FEM) solution of the 1-D ordinary differential equation governing the spectrum of the layered-media Green’s function with spatial $h$ -adaptive meshing. The resulting pole-residue form of the Green’s function spectrum enables analytic evaluation of the pertinent Sommerfeld integrals providing $O(h^{p})$ error control of the spatial layered-medium Green’s function in near, intermediate, and far zones. The detailed error analysis is presented enabling automation of the 1-D FEM mesh refinement, which guarantees a prescribed accuracy of the solution depending on the distance between the source and observation locations. The method is well suited for computing Green’s function databases used by method of moments capacitance and inductance extractors.

A hybrid discretization scheme for solution of volume integral equation (VIE) by method of moments (MoM) for electromagnetic scattering from dielectric objects is proposed in this article. The Schaubert-Wilton-Glisson and edge (SWG-Edge) hybrid basis functions are used in this discretization scheme. According to the divergence-free condition of electric displacement vector, a kind of edge basis functions defined in elements including boundary faces which separate a dielectric object from the background is derived. As a result, we get a SWG-Edge hybrid basis set. Details for the calculation of the corresponding matrix elements for the edge basis and testing functions are presented. Numerical results show the validity and accuracy of the hybrid discretization scheme. Finally, the proposed method is used for efficient solution of VIE for inhomogeneous dielectric objects with multiboundary. It is shown that for multiboundary problems, the number of unknowns of the hybrid basis is only about 71% of the traditional SWG basis. This means that the memory for solution of VIE by the traditional SWG basis functions can be reduced by half. Therefore, the SWG-edge hybrid basis is much more efficient than the traditional SWG basis for solution of VIE with multiboundary problems.

To efficiently solve the electromagnetic scattering problems over a wide incident angle, a novel scheme by introducing the two-dimensional compressive sensing theory into the wavelet method of moments is proposed. In this scheme, a linear system of equations with multiple right-hand sides in wavelet domain is formed firstly, and one side of the bilateral sparse transform to the induced current matrix is simultaneously accomplished and then the bilateral measurement of the induced current matrix is operated by the linear superposition of the right-hand side vectors a few times and the extraction of rows from the impedance matrix. Finally, after completing the other side of the bilateral sparse transform, the wide-angle problems can be solved rapidly by two times of recovery algorithm with prior knowledge. The basic principle is elaborated in detail, and the effectiveness is demonstrated by numerical experiments.

To efficiently analyze the electromagnetic scattering from composite perfect electric conductor (PEC)-dielectric objects with coexisting closed-open PEC junctions, a modified hybrid integral equation (HIE) is established as the surface integral equation (SIE) part of the volume surface integral equation (VSIE), which employs the combined field integral equation (CFIE) and the electric field integral equation (EFIE) on the closed and open PEC surfaces, respectively. Different from the traditional HIE modeled for the objects whose closed and open PEC surfaces are strictly separate, the modified HIE can be applied to the objects containing closed-open junctions. A matrix equation is obtained by using the Galerkin’s method of moments (MoM), which is augmented with the spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA), improved by the mixed-potential representation and the triangle/tetrahedron-based grouping scheme. Because in the improved SE-MLFMA, the memory usage for storing the radiation patterns of basis functions is independent of the SIE type in the VSIE, it is highly appropriate for the fast solution of the VSIE that contains the HIE. Various numerical experiments demonstrate that during the calculation of composite objects containing closed-open PEC junctions, the application of the modified HIE in the VSIE can give reliable results with fast convergence speed.

For electromagnetic scattering analysis of inhomogeneous dielectric objects over a wide incident angle, method of moments is used to solve volume integral equation (VIE), and a special excitation source with multiple incident angles information based on compressive sensing is introduced into the VIE so as to construct a fast solving model to reduce the number of repeated calculations of the matrix equation. By the analysis of computational complexity, the computational cost of the proposed method is significantly lower than that of the traditional method, and the effectiveness of the proposed method is verified by the simulation experiments of the inhomogeneous dielectric objects with different structures.

This letter presents a rotation-based optimization method for pattern synthesis of subarrayed phased arrays. In order to keep a good beam scanning ability at different steering angles, the optimization problem is reasonably defined where the objective is taken as minimizing the maximum sidelobe level at a series of steering angles, and both the arrangement variables and the scanning variables are optimized simultaneously. The mutual coupling of the iteratively rotated arrays is rigorously considered in the synthesis. In order to solve the synthesis problem effectively, the design sensitivities are derived analytically and the synthesis is actualized by using a gradient-based algorithm. Typical examples, with considering different regular subarray configurations and the state-of-art irregular subarray configurations, are provided to validate the effectiveness of the proposed approach.

Electromagnetic scattering model from 3-D snowpack with arbitrary thickness is considered. A fully coherent model is presented through the usage of the Statistical S-Matrix Wave Propagation in Spectral Domain approach (SSWaP-SD). The computer-generated snow media is constructed using 3-D spatial exponential correlation function along with Lineal-Path function to preserve the connectivity of the snow particles as well. The SSWaP-SD in conjunction with a Method of Moments (MoM) code based on the discrete-dipole approximation (DDA) is chosen to leverage both the time-efficient computations of the DDA and the full-coherency of the SSWaP-SD method simultaneously. The SSWaP-SD depends on the discretization of the medium into thin slabs. Several realizations of a thin snow slab are solved numerically to form the statistics of the scattering matrix representing such a thin snow layer. For an arbitrarily thick snow layer, thin slabs of a snowpack are analyzed and a corresponding polarimetric N-port (representing different directions of scattering) S-matrix is generated. These S-matrices are cascaded using SSWaP-SD method to calculate the total forward and backward bistatic scattered fields in a fully coherent way. The simulation results of the backscattering from an arbitrary thick snow layer are presented and validated with measurements.

This chapter presents the concept of the Cauchy method for the interpolation and extrapolation of data. The Cauchy method is to interpolate and extrapolate the data from calculating coefficients simultaneously of the numerator and denominator polynomials which are used to approximate the data by a ratio of two polynomials. The usefulness of the Cauchy method is demonstrated for the ease in which it can be incorporated into a Method of Moments program to speed up the computation process over a broad band. The Cauchy method can also be used in the analysis of filters over a broad frequency range. An application of the Cauchy method is in creating a data‐base of many devices working in varying operating conditions. A fast and accurate interpolation algorithm is proposed to reconstruct the high resolution amplitude‐only frequency domain response such as radar cross section and antenna radiation patterns from sparse and non‐uniform samples based on the Cauchy method.

A stable volume integral equation (VIE) solver based on polarization/magnetization currents is presented, for the accurate and efficient computation of the electromagnetic (EM) scattering from highly inhomogeneous and high contrast objects. We employ the Galerkin method of moments to discretize the formulation with discontinuous piecewise linear basis functions on uniform voxelized grids, allowing for the acceleration of the associated matrix-vector products in an iterative solver, with the help of FFT. Numerical results illustrate the superior accuracy and more stable convergence properties of the proposed framework, when compared against standard low-order (piecewise constant) discretization schemes and a more conventional VIE formulation based on electric flux densities. Finally, the developed solver is applied to analyze complex geometries, including realistic human body models, typically used in modeling the interactions between EM waves and biological tissue.

In this letter, we present research on the application of deep neural networks to predicting macro basis functions for complicated computational electromagnetics problems. We provide error statistics and representative examples for networks trained on simple and complicated datasets of method of moments scattering problems. Notably, we demonstrate that the networks learn generalizable knowledge applicable to problem types on which they were not trained. We conclude that the networks produce encouraging results, especially for cross validation, and larger training datasets will improve reliability for general scattering problems.

To solve scattering from multiple complex targets above the rough surface with a high root mean square, a hybrid method combining real coefficients fitting both Green's function and its gradient with the fast Fourier transform (RFGG-FG-FFT) and the iterative Kirchhoff approximation (IKA) is developed. Due to its great performance for solving complex fine structures, RFGG-FG-FFT is applied to compute scattering from complex targets, while IKA is used to solve scattering from rough surface. Interactions between the targets with rough surface are solved iteratively and these are the most time-consuming part of the entire computational process. To overcome this computational bottleneck, the combined multilevel fast multipole algorithm (MLFMA), ray-propagation fast multipole algorithm (RPFMA), and fast far-field approximation (FAFFA) are incorporated into interactions between the targets and rough surface. To effectively implement the MLFMA-RPFMA-FAFFA algorithm, the rough surface region is divided into near area, adjacent area, and far area according to distance, where the interactions between these areas with targets are solved by MLFMA, RPFMA, and FAFFA, respectively. The high efficiency and accuracy of the proposed method are verified by a comparison with the numerical method.

To effectively solve the electromagnetic scattering or radiation properties from the perfect electric conductor objects containing closed–open surface junctions, how to establish the hybrid combined field integral equation–electric field integral equation (CFIE–EFIE) is studied, which is different from the existing scheme for the objects, where the closed and open parts are separate. Furthermore, it is found that when the integral equation is solved using the method of moments, if the widely used RWG basis functions are employed to expand the induced surface current, the CFIE–EFIE may give inaccurate numerical results for the objects containing fine structures. The numerical accuracy can be improved by introducing the linear–linear (LL) basis functions. Moreover, to pursue a high computational efficiency, the LL and RWG basis functions are simultaneously used to expand the current on the fine structures and other relatively smooth surfaces, respectively, whose validity is verified by the numerical results.

Electromagnetic scattering and emission from 1-D rough surfaces with multiple elevations are studied using full-wave simulations. Both the root-mean-square (rms) heights and the surface length are large compared to the wavelength. A novel multilevel steepest decent-sparse matrix canonical grid (MLSD-SMCG) method is proposed to address limitations in the original SMCG. The uniform Nystrom method and neighborhood impedance boundary condition (NIBC) are also incorporated in solving the dual surface integral equations (SIEs) of the method of moments (MoM). Simulation results are illustrated at L-band for soil and ocean surfaces. The surface rms heights and lengths are up to 1.43 and 243.8 m corresponding to 6 and 1024 wavelengths at 1.26 GHz, respectively. For ocean surfaces, the wind speeds up to 20 m/s are considered, and the entire spectrum is included to capture all relevant surface length scales. Numerical results indicate the proposed approach is computationally efficient and accurate. Energy conservation checks in simulations are at $10^{-4}$ for ocean scattering and emission. Also, the effects of wind-driven roughness on ocean emissivity are further investigated using the proposed approach in terms of wind speed and observation angle for both polarizations.

The numerical solution of the electric field integral equation in electromagnetic scattering problems involving metallic bodies, using the method of moments in conjunction with the fast multipole method, gives rise a full matrix with highly spread complex eigenvalues and consequently with a low condition number. Thus, iterative methods may not converge or it will require an extremely large number of iterations, which make this strategy unfeasible due to the high solution time and the expensive computational resources required. To overcome this drawback, the system matrix must be preconditioned to ensure the convergence in a reasonable number of iterations and with appropriate accuracy. In this work, some preconditioning techniques are revised and applied to a linear equation system derived from such type of problems, and the performance of these preconditioners is estimated and analyzed comparatively using the generalized minimal residual iterative method.