Search

The finite-difference frequency-domain (FDFD) method has important applications in the wave simulation of various wave equations. To promote the accuracy and efficiency for wave simulation with the FDFD method, we have developed a new 27-point FDFD stencil for 3D acoustic wave equations. In the developed stencil, the FDFD coefficients depend not only on the ratios of cell sizes in the x-, y-, and z-directions but also depend on the spatial sampling density (SD) in terms of the number of wavelengths per grid. The corresponding FDFD coefficients can be determined efficiently by making use of the plane-wave expression and the lookup table technique. We also develop a new way for designing an adaptive FDFD stencil by directly adding some correction terms to the conventional second-order FDFD stencil, which is simpler to use and easier to generalize. Corresponding dispersion analysis indicates that, compared to the optimal 27-point stencil derived from the average-derivative method (ADM), the developed adaptive 27-point stencil can reduce the required SD from approximately 4 to 2.2 points per wavelength (PPW) for a cubic mesh and to 2.7 PPW for a general cuboid mesh. Numerical examples of a 3D homogeneous model and SEG/EAGE salt-dome model indicate that the developed stencil is more accurate than the ADM 27-point stencil for cubic and general cuboid meshes, while requiring similar CPU time and computational memory as the ADM 27-point stencil for direct and iterative solvers.

An efficient and accurate hybrid spectral element-spectral integral (SESI) method is proposed to simulate electromagnetic (EM) scattering by objects in multiregion cylindrically layered media. The field in each of the multiple regions with multiple scatterers can be solved by the spectral element method (SEM), while the spectral integral method (SIM) is used as an exact boundary condition for the adjacent regions with multilayered media. This boundary condition between the electric field and the surface current density in each cylindrical layer can be obtained by using a recursive formula in SIM. The inverse matrix of a Toeplitz matrix arising from the SIM can be solved by the fast Fourier transform (FFT) with $O(N\log N)$ complexity. The hybrid SESI method is used to simulate homogeneous and/or inhomogeneous multiregion multilayered structures. Numerical examples, including the frequency selective surface (FSS) applications, demonstrate that the hybrid SESI method is efficient and accurate by comparing its results with analytical solutions and results from the conventional SEM and the finite element method (FEM).

We have used the spectral-element method (SEM) to simulate 3D acoustic wavefields in the fluid-filled borehole embedded in fractured media. The fractures are characterized by the linear-slip model (LSM), which is incorporated into the surface integral of the SEM weak form, avoiding meshing individual fractures, thus reducing the degrees of freedom of the fractures compared with meshing each fracture directly. For the fracture-free case, we validate SEM through the comparison with the real-axis integration method for monopole and dipole sources. For the case with a fracture, we compare the SEM-LSM solutions with the reference numerical solutions of a thin-layer model using the finite-difference method. Good agreement is achieved between the results from our method and the reference finite-difference solutions. We find that the acoustic wavefields excited by a dipole source are more sensitive to the fractures than those by a monopole source. To show the ability of the approach to handle complex problems, we simulate the cases with a tilted fracture and multiple fractures. Based on the simulated results, we investigate the influence of the fracture parameters (e.g., stiffness, tilt angle, azimuth, thickness, number, and spatial intervals of fractures) on the scattered wavefields. We find that the tilt angle has an obvious influence on the scattered waveforms and amplitudes. The results also demonstrate that the wavefields are quite sensitive to the number of fractures. The magnitudes of the horizontal components’ transmitted wavefields decrease linearly with the number of fractures. Through analyzing the synthetic data in the time and frequency domains, we discuss how to evaluate the properties of fractures intersected by a borehole.

Solving the Helmholtz equation has important applications in various areas, such as acoustics and electromagnetics. Using an iterative solver together with a proper preconditioner is key for solving large 3D Helmholtz equation. The performance of existing Helmholtz preconditioners usually deteriorates when the minimum spatial sampling density is small (approximately four points per wavelength [PPW]). To improve the efficiency of the Helmholtz preconditioner at a small minimum spatial sampling density, we have adopted a new preconditioner. In our scheme, the preconditioning matrix is constructed based on an adaptive complex frequency that varies with the minimum spatial sampling density in terms of the number of PPWs. Furthermore, the multigrid V-cycle with a GMRES smoother is adopted to effectively solve the corresponding preconditioning linear system. The adaptive complex frequency together with a GMRES smoother can work stably and efficiently at different minimum spatial sampling densities. Numerical results of four typical 3D models show that our scheme is more efficient than the multilevel GMRES method and shifted Laplacian with multigrid full V-cycle and a symmetric Gauss-Seidel smoother for preconditioning the 3D Helmholtz linear system, especially when the minimum spatial sampling density is large (approximately 120 PPW) or small (approximately 4 PPW).

SUMMARY Simulating poroelastic waves in large-scale 3-D problems having porous media coupled with elastic solids and fluids is computationally challenging for traditional methods. It is well established that the spectral element method (SEM) is more effective than the traditional methods like the finite element method (FEM) when dealing with complex geophysical problems, for its high-order accuracy with exponential convergence. However, at present, little research has been done for SEM in the frequency domain, which will be more efficient than the time-domain SEM for narrowband simulations with multiple sources, material dispersion and attenuation. Herein, we systematically develop a SEM in the frequency domain to simulate coupled poroelastic, elastic and acoustic waves in anisotropic (i.e. porosity, permeability and elastic coefficients with anisotropy), heterogeneous, and lossy media. Furthermore, we completely remove the dimension inconsistency between the displacement field and the pressure in porous media to reduce the condition number of the system matrix by around 16 orders of magnitude while maintaining the symmetry of the system matrix. To solve the multiphysics coupling problems, we apply different coupling conditions to different interface types, and use basis functions to discretize the corresponding governing equations. Numerical examples show that the proposed SEM can obtain higher accuracy with much fewer unknowns compared with the FEM and has the capacity to solve the large-scale real coupling problems.

In this letter, the mixed finite element method (Mixed FEM) incorporating with the surface current boundary condition (SCBC) is firstly proposed to perform eigenmode numerical simulations of graphene-based plasmonic waveguides. The SCBC which is based on modeling graphene as the zero-thickness conductive sheet, is introduced to reduce the extremely fine discretization of graphene at the atomic scale. Thus, enormous unknowns and computational resources are significantly decreased in the proposed new method. Numerical examples of some typical graphene-based waveguides are presented to verify numerical accuracy and computational efficiency of the new method.

In practical applications, electromagnetic measurements often contain damaged data due to malfunctioning receivers, which can severely influence the inversion performance. Thus, in this letter, a new receiver approximation machine learning (RAML) method is proposed to repair the data from the damaged receivers and the repaired data are the input to the dual-module nonlinear mapping module–image enhancing module machine learning scheme for the 2-D inverse scattering problem. The RAML method has been tested for the inversion of both measured transverse electric and transverse magnetic datasets provided by Institute Fresnel. Excellent inversion performance has been obtained when 10 out of 241 (4.15%) receivers are damaged. Furthermore, in an extreme situation, the RAML method can also have good inversion performance even though half of the receivers are damaged.

Borehole and fracture in well-logging applications are usually simulated by the finite-element method (FEM) or volume integral equation (VIE). In this work, we propose the surface integral equation (SIE) to simulate them together. Specifically, the borehole is treated by the Poggio, Miller, Chang, Harrington, Wu, and Tsai (PMCHWT) formulation, whereas the fracture is handled by the thin dielectric sheet (TDS)-based SIE, i.e., TDS-SIE. The notorious low-frequency breakdown of PMCHWT is cured by using loop and tree basis functions for discretization. The hybridization of the loop-tree enhanced PMCHWT and TDS-SIE may be referred to as LT-TDS, which is reported for the first time. Moreover, we extend LT-TDS into the case where the background is a layered medium (LM), leading to the more universal and powerful solver entitled LM-LT-TDS. We validate the proposed (LM-)LT-TDS by simulating several low-frequency examples and comparing with the reference results obtained by FEM. Of particular concern is a practical well-logging case where both the borehole and the tilted fracture straddle a three-layer medium.

We propose a hybrid method based on the finite-difference time-domain (FDTD) algorithm and analytical methods to solve the elastic scattering of 3-D objects outside a borehole. In the proposed method, the FDTD algorithm containing the incident waves generated by a borehole acoustic source is first used to calculate the wave fields inside a rectangular volume enclosing the object. Then, the reciprocity theorem for the wave fields in the fluid/solid configurations is employed to transform the near fields around the object into the far fields inside the borehole. This method uses the regional domain which tightly encloses the object, thus avoiding the simulation for the whole domain and leading to high efficiency for the large-scale and multiscale problems containing both the borehole and far-field objects. The validations with both analytical solutions and independent numerical methods demonstrate the accuracy and efficiency of the hybrid method.

It is difficult to realize a traveling wavemode current on a single conductor loop to generate a wideband circularly polarized (CP) radiation wave using a single feeding structure. In this communication, with the help of the characteristic mode analysis, we cut a wide gap in the annular ring conductor patch and design the feeding structure with capacitive coupling effect on the patch. By this way, the annular patch is effectively distributed with traveling wave currents and a printed annular ring antenna operating in the 2.4 GHz band is constructed. The experimental results show that the proposed antenna can generate CP radiation with impedance and axial ratio bandwidths of 26% and 10.6%, respectively. Meanwhile, this antenna has a good structural tolerance capability.

This letter presents a filtering substrate integrated waveguide slot antenna design with multiple radiation nulls based on a double slot coupling scheme. It consists of a dual-layer cavity resonator, a slot in the first layer, and two coupling slots inserted in the middle layer. The slot in the first layer functions as the antenna radiator. This radiator is etched in the first cavity instead of the last stage of the network, resulting in two radiation nulls. A double slot coupling scheme is employed in the middle layer to not only couple the two-layer cavity resonators but also generate two more radiation nulls. Owing to these radiation nulls, the antenna features high-frequency selectivity as well as out-of-band radiation suppression level. For demonstration, the proposed filtering antenna is implemented and tested. The antenna operates at the center frequency 4.5 GHz with 15.4% (4.2–4.9 GHz) measured bandwidth. The maximum gain within the operating band is 7.5 dBi and four radiation nulls are generated. Better than 21 dB out-of-band radiation rejection level is obtained.

The simulation of electromagnetic fields in many applications with double periodicity can be viewed as an image-to-image translation problem, where the structure is known and the fields need to be predicted. In this work, we take extreme ultraviolet (EUV) lithography as an example and propose a very efficient technique based on the U-Net architecture, a deep fully convolutional network (FCN). The U-Net is trained with data of some typical patterns in a 128 nm $\times\,\,128$ nm unit cell, and good accuracy can be obtained in the prediction of the near field on much larger unit cells with complex patterns. Furthermore, numerical experiments demonstrate that the proposed method is three orders of magnitude faster than conventional state-of-the-art methods, such as the spectral-element spectral-integral method.

Electromagnetic imaging of inhomogeneous objects is a nonlinear inverse scattering problem which can be effectively handled by means of linear inversion methods or nonlinear optimization methods. In addition to being nonlinear, inverse scattering problems are also ill-posed which can be overcome through a regularization scheme by taking into account some kind of $a$ priori information. However, it is not straightforward to incorporate such inhomogeneity prior information into conventional inversion methods. In this work, we propose an innovative method to solve the problem of imaging inhomogeneous objects with piecewise homogeneity. Under Born approximation (BA), this problem is cast into a linear inversion one which is then addressed by means of a hierarchical Bayesian inversion method. To account for the piecewise homogeneity of the image, a Gaussian mixture model (GMM) is developed to enforce the feature. Specifically, a hidden label variable which is associated with each pixel is introduced for the class of materials and the contrast of each pixel is modeled as a mixture of independent Gaussian priors. Then, the proposed hierarchical Bayesian inversion method incorporates the GMM to the variational Bayesian inference framework to approximate the posterior distribution of all the unknowns (the unknown contrast, hidden label variable, and other model parameters). In addition, the damped generalized approximate message passing (GAMP) is utilized to circumvent the matrix inversion, making the overall process very computationally efficient. Extensive numerical examples will be shown to demonstrate the effectiveness of the proposed method.

A volume equivalent shooting and bouncing ray (VESBR) method is proposed to analyze the electromagnetic scattering of dielectric and composite objects with thick dielectric medium. Different from traditional high-frequency methods which utilize surface sources, this VESBR considers the propagation of electromagnetic waves inside the dielectric media and introduces volume equivalent sources to calculate the scattering fields. Compared with traditional methods, two different problems need to be solved in this method, i.e., the ray tracing on dielectric boundary and the volume integral in ray tube. For ray tracing process, a refined formula is proposed to acquire the information of reflection waves and transmission waves on dielectric boundary. For volume integral in ray tube, the integral is transformed to five surface integrals based on Gauss’s law. The simulations of four cases show that the results of VESBR agree well with those of surface integral equation (SIE), while the computation time and the required memory of VESBR are much less than those of SIE.

In this letter, the mixed $L_1$ – $L_2$ norm regularization is adopted to constrain the full-wave inversion solution of the multiparametric electromagnetic inverse scattering by the 3-D anisotropic objects. The mixed $L_1$ – $L_2$ regularization term is added to the standard $L_2$ norm cost function in the framework of the Born iterative method. In each iteration, the mixed $L_1$ – $L_2$ norm term is transformed into $L_2$ norm term through a weight matrix and the whole cost function is minimized by the conjugate gradient method. Numerical results show that, compared with the traditional Tikhonov $L_2$ regularization, the mixed $L_1$ – $L_2$ regularization can achieve higher reconstruction accuracy without additional computational cost due to the structural similarity constraint among different model parameters.

Superoxide dismutase (SOD) is a crucial reactive oxygen species (ROS) scavenger, which converts superoxide radical to H2O2, so it is thought to enhance abiotic stress tolerance by reducing ROS and thus avoiding oxidative damage. In this study, we isolated a salt- and oxidative stress-responsive copper-zinc (Cu/Zn) SOD encoding gene TaSOD5 from wheat. The ectopic overexpression of TaSOD5 in Arabidopsis thaliana increased total SOD and Cu/Zn SOD activities and enhanced tolerance to salt stress. Arabidopsis ectopically expressing TaSOD5 possessed a superior resistance to oxidative stress stimulated by exogenous H2O2. Ectopic overexpression of TaSOD5 elevated the activities of both ROS scavengers and an O2.- producer - NADPH oxidase. These findings show that Cu/Zn SOD enhanced salt tolerance via regulating the machinery of redox homeostasis rather than improving SOD activity alone.

Two mixed spectral-element methods (MSEMs) are proposed to solve Maxwell’s eigenvalue problems with Bloch (Floquet) periodic and open resonators to remove the dc spurious modes present in the traditional numerical methods. The first MSEM combines the variational form of Gauss’s law to make the electric field satisfy the divergence-free condition. This method does not need to modify the Arnoldi algorithm for the eigenvalue problems, but the number of degrees of freedom (DOFs) is larger than that of the traditional spectral-element method (SEM). The second MSEM, as a generalization of the tree–cotree technique, can eliminate the dc spurious modes by imposing the constrained equations on the Ritz vectors in the Arnoldi algorithm without increasing the DOF from the traditional SEM. We expand the electric field in terms of the edge basis functions associated with the cotree edges and the gradient of the nodal basis functions so that the discrete gradient matrix $\bar {\bar {\mathrm {G}}}$ consists of the identity matrix $\bar {\bar {\mathrm {G}}}_{t}$ and the zero matrix $\bar {\bar {\mathrm {G}}}_{c}$ , making the matrix inversion of $\bar {\bar {\mathrm {G}}}_{t}$ trivial. Finally, in the numerical experiments, we compare the computational costs of the MSEMs and finite-element method (FEM) in COMSOL to illustrate the high efficiency of the MSEMs.

We demonstrate a new variety of spoof surface plasmon polariton (SSPP) waveguides and notch filters with periodic arrays of ultra-thin metallic meander-strip units for high-efficiency and strong confinement microwave SSPPs transmission and notch rejection. Firstly, the dispersion characteristics of the proposed SSPPs waveguide based on meander-strip units are investigated. The dispersion curve of the proposed waveguide presents a unique negative group velocity characteristic, and the asymptotic frequency greatly reduces to near half as that of SSPP waveguide based on traditional rectangular-grooved units with the same transverse size. To validate the proposed design, an SSPP waveguide prototype is fabricated and tested, showing good lowpass filtering performances with a high transmission coefficient ( $\text {S}21 > {-}1$ dB) and a low reflection coefficient ( $\text {S}11 dB) below the asymptotic frequency of 5.2 GHz. Based on this waveguide structure, a notch filter is designed by loading a split ring resonator (SRR). The transmission coefficient (S21) of this filter is −18 dB at the notch frequency of 2.52 GHz. Furthermore, a PIN diode is integrated into the SRR of the notch filter to make the notch frequency switchable. As the PIN diode turns from the ON state to the OFF state, the notch frequency switches from 2.5 GHz to 3.5 GHz. The proposed waveguides and notch filters with electronically adjustable functionalities may have great potential applications in microwave integrated plasmon circuits and programmable systems.

Different from the conventional phased array radar, a frequency diverse array (FDA) applies additional frequency shift across the array elements, yielding a range–angle-dependent transmit beampattern that provides a huge potential opportunity for target estimation and range-dependent clutter and interference suppression. Generally, the conventional FDA employs a linear small frequency increment, forming a time-varying “S”-shape range–angle beampattern, which is range–angle coupled. In this article, a range–angle transmit beampattern synthesis method for FDA based on frequency offset optimization is proposed. Particle swarm optimization (PSO) is adopted in the FDA element frequency increment design to achieve a dot-shaped transmit beampattern. Meanwhile, matched weights are designed for time-modulation compensation. Numerical simulation results demonstrate that the proposed approach achieves better time-invariant performance over other FDA frameworks.

A combination of the mixed finite-element time-domain method (MFETD) and SPICE solver is proposed in this letter to analyze the circuit response and crosstalk effects in complex microwave circuits with linear/nonlinear, passive/active components. The MFETD method in the EM part is adopted as an unconditionally stable time integration scheme to account for the low-frequency breakdown problem. SPICE is introduced to solve the nonlinear circuit equations in the circuit part by taking into account the coupling between multiport circuits. A microwave circuit based on an AD633 chip and an MCP3221 board is simulated to verify that this hybrid MFETD-SPICE method not only is superior in mesh flexibility to the finite-difference time-domain (FDTD)-based method but also exploits the well-developed open-source software SPICE to solve the nonlinear equations.

A hybrid method is proposed to reconstruct the subsurface 3-D objects with electromagnetic fields. The frequency-domain reverse time migration (FRTM) is first used to determine the approximate locations and sizes of the objects. Then, based on these results, the full-wave inversion, the variational Born iteration method (VBIM) is used to reconstruct both the shapes and dielectric parameters of the objects. The Monte Carlo method (MCM) is adopted to further refine the reconstructed shapes. Numerical simulations show that the proposed hybrid method can be effectively used for the subsurface imaging and detection.

An all-dielectric nanoantenna is expected to greatly boost the nonlinear performance owing to its large mode volume and low material loss. However, it still suffers from the relatively weak near-field enhancement and the inferior far-field directivity. In this work, by successively introducing an upper metal ring and a bottom metal film, the plasmonic resonance and the perfect electric conductor (PEC) mirror effect are employed to significantly enhance and tailor the third harmonic generation (THG) from the high-index silicon nanoantenna. Numerical results show that benefiting from both of these two metal components, not only the THG efficiency is increased by more than 1 and 3.5 orders of magnitude compared with those with only single metal component and without any metal component, respectively, but also an improved radiation directivity can be obtained. The dependences of geometric parameters are discussed as well. This work suggests a route to enhance and manipulate the nonlinear radiation by a hybrid nanoantenna and facilitates its practical applications such as biosensing and nonlinear light sources.

The series-fed subarray still plays a critical role in a partially-corporate-fed array, which has advantages over the corporate feed one in terms of both beam steerability and freedom in array sizes. In this paper, two techniques are presented for the wideband design of series-fed waveguide slot arrays. Firstly, the overload technique is adopted to design standing-wave fed 1 $\times $ 4-element arrays of both coupling slots and radiating slots. The simulated bandwidths for $\vert S_{11}\vert dB are enhanced to 8.1% and 12.2%, respectively. Secondly, the open-cavities, namely decoupling structures above radiating slots, are introduced to suppress the mutual couplings among a $4\times4$ -element array. Its bandwidth for $\vert S_{11}\vert dB is significantly improved from 5.1% to 11.3%. For demonstration, a $4\times4$ -element array is designed in the X-band, and is fabricated by Direct Metal Laser Sintering technique. The measured bandwidths for $\vert S_{11}\vert dB and the antenna efficiency higher than 70% are as wide as 12.4% and 9.5%, respectively. The validity of those wideband design techniques is verified.

The spectral element method (SEM) is widely used for analyzing high frequency electromagnetic wave propagation and scattering in complex structures. At low frequencies, however, the primary (direct) fields are usually much larger than the secondary fields caused by scattering, thus making it much more difficult to accurately simulate the secondary (scattered) fields because of the source singularity in the primary fields. To more effectively and accurately simulate the low-frequency secondary fields in subsurface structures, in this work the vector Helmholtz equation for the scattered fields is used to directly obtain the secondary field data in inhomogeneous anisotropic media. The computational method for the secondary electromagnetic fields is based on the mixed spectral element method (mixed SEM) for anisotropic objects in a layered anisotropic background medium. The electromagnetic field is separated into the background fields that are evaluated analytically using the dyadic Green’s functions (DGFs) of a layered uniaxially anisotropic medium, and the secondary fields caused by anomalous bodies with arbitrary shapes are numerically computed by the mixed SEM. This avoids the source singularity, and allows the transmitters to be located outside the computational domain. By enforcing Gauss’ law as the constraint condition, the mixed SEM efficiently eliminates the low frequency breakdown problem. Numerical results verify the proposed method over the traditional SEM in low-frequency scattering from objects in subsurface layered anisotropic media.

A compact and broadband omnidirectional antenna is proposed for quad-polarization diversity. Novel reconfigurable structures of omnidirectional vertical polarization (VP) and horizontal polarization (HP) elements based on embedded design are put forward to achieve low-profile. A simplified equivalent LC cascaded circuit is modeled to better understand the broadband VP element and guide its design. In order to realize quad-polarization diversity, an advanced switchable feed network, which contains ten p-i-n diodes with four output states are carefully designed. Measured results show that the overlapped bandwidth for all operation modes is 20.5% (2.28–2.8 GHz) within a compact size of 0.69 λ 0 × 0.69 λ 0 × 0.064 λ 0, where λ 0 is the free-space wavelength at the center frequency 2.5 GHz.