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Method of moments (MoM) is a classical numerical method for analyzing electromagnetic (EM) scattering from various objects. Generalized minimal residual (GMRES) is a kind of widely used solver for linear systems of equations generated by MoM, whose calculation complexity mainly includes two parts, matrix-vector multiplications and the orthogonalization procedure. In order to accelerate the solution of matrix equations arising in MoM, an efficient strategy for constructing nonorthonormal Krylov bases is proposed in this article, which can be introduced into standard GMRES and its variants (e.g., GMRES($m$) and quasi-GMRES) and can be easily combined with the fast approaches for MOM (e.g., FMM and ACA). The principle of the method is described in detail, and the effectiveness is verified by numerical results. [ABSTRACT FROM AUTHOR]

We present a new numerical scheme to solve efficiently scattering problems involving an elongated and flat heterogeneous dielectric material assumed to be invariant along a direction of space. The technique consists of compressing the integral operators of an integro-differential formulation with a so-called quantized tensor train (QTT) algorithm whose use is rather original in this context. We show that it allows to compute and store operators with a notably small memory footprint while having at the same time a fast matrix-vector product (MVP) leading to a competitive method compared with the more classical $\mathcal {H}$ -matrix approach. [ABSTRACT FROM AUTHOR]

A conversion matrix approach to solving network problems involving time-varying circuit components is applied to the method of moments for electromagnetic scattering analysis. Detailed formulations of this technique’s application to the scattering analysis of structures loaded with time-varying circuit networks or constructed from general time-varying media are presented. The computational cost of the method is discussed, along with an analysis of compression techniques capable of significantly reducing the computational cost for partially loaded systems. Several numerical examples demonstrate the capabilities of the technique and validate it against conventional methods of modeling time-varying electromagnetic systems, such as finite difference time domain and transient circuit co-simulation. [ABSTRACT FROM AUTHOR]

A butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly (HOD-BF) scheme to construct the system matrix and obtain its approximate inverse, used as a preconditioner. Complexity analysis and numerical experiments validate the $O(N\log ^{2}N)$ construction cost of the HOD-BF-compressed system matrix and $O(N^{1.5}\log N)$ inversion cost for the preconditioner, where $N$ is the number of unknowns in the high-frequency EM scattering problem. For many practical scenarios, the proposed VIE solver requires less memory and computational time to construct the system matrix and obtain its approximate inverse compared to a $\mathcal {H}$ matrix-accelerated VIE solver. The accuracy and efficiency of the proposed solver have been demonstrated via its application to the EM analysis of large-scale canonical and real-world structures comprising of broad permittivity values and involving millions of unknowns. [ABSTRACT FROM AUTHOR]

In this article, a novel beam shaping technique is developed to synthesize the array factor (AF) radiation pattern of linear and planar antenna arrays. The proposed method is established based on the expanding of AF using Legendre transform in conjunction with an integrand operator. A system of linear equations is derived and its solution is obtained using least-square method (LSM) for the required pattern. In addition, an iterative procedure is introduced to reduce the number of elements of the primary designed array for a specified mean square error (mse). Then, the proposed method is applied to synthesize the AF of planar and ring antenna arrays. To verify the performance of the proposed method, a few comprehensive well-known linear, planar, and ring arrays are examined. The obtained results show that the introduced method can be used to design the AF pattern of many types of practical arrays with good accuracy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

First, an acceleration to compute the impedance matrix obtained from the electric field integral equation (EFIE) discretized by the Galerkin method of moments (MoM) with Rao–Wilton–Glisson basis functions is addressed. It is based on a far-field approximation and makes it possible to avoid looping on the source and observation triangles. Next, the impedance matrix is split into strong and weak interactions; the latter is compressed by expressing it from Toeplitz submatrices. Then, the linear system is efficiently solved by a bi-iterative scheme. For a given order, the least-squares QR (LSQR) algorithm is applied to solve the sparse linear system related to the strong interactions, while the matrix–vector products, related to the weak interactions, are accelerated by using FFTs. Numerical results of the field scattered by perfectly conducting paraboloid-shape object and Gaussian rough surface are shown. [ABSTRACT FROM AUTHOR]

The distorted Born iterative method (DBIM) is widely used in microwave imaging to solve the electromagnetic inverse scattering problem iteratively based on the distorted Born approximation. Various methods are used for the forward solver in the DBIM to simulate wave propagation and scattering. In this communication, a new matrix building technique exploiting the basis functions of the finite element method (FEM) is used to create the inverse-problem matrix in a 2-D DBIM algorithm. The proposed approach provides great efficiency as the entries of this matrix are readily calculated from already precomputed matrices in the FEM procedure without the need for interpolation to calculate the field. The FEM-based DBIM is validated with both simulated data and experimental data from a microwave tomography (MWT) system. Results confirm that the proposed FEM implementation can be an efficient and accurate forward solver for this MWT system. [ABSTRACT FROM AUTHOR]

We present a multifilament current method (MFCM) incorporated with generalized sheet transition condition (GSTC) to simulate 2-D cylindrical metasurfaces with arbitrary cross sections. The GSTC casts in the form of an impedance-type boundary condition to relate the tangential fields on two sides of a cylindrical metasurface. The MFCM is subsequently introduced and formulated by employing the GSTC. The doublet-current unit, including both electric and magnetic filamentary sources, is introduced in order to capture both co- and cross-polarized scattered and transmitted fields from the GSTC characterized cylindrical metasurfaces. Three illustrative examples are presented to validate the proposed simulation technique. The behaviors of filamentary sources in terms of scattered field singularities and the ill-conditioning issue of the constructed matrix are also discussed in detail. In comparison to existing numerical methods, the proposed technique has its merits on simplicity and conciseness. [ABSTRACT FROM AUTHOR]

Bounds on the frequency domain behavior of electrically small antennas are adapted to assess the time-domain distortion or fidelity achievable by simple linear time-invariant (LTI) systems. Rigorous expressions for a TM01 spherical shell are used as a direct analog to the well-known Chu limit on an antenna’s bandwidth-efficiency product. These expressions are shown to agree with results obtained using narrowband single resonance approximations, allowing for the analysis of arbitrary small dipole-like structures through bounds on their single-frequency Q-factor and efficiency. The resulting expressions are used as a basis for assessing the performance gains of electrically small non-LTI (e.g., direct antenna modulation) transmitters for which Q-factor and impedance bandwidth are not defined but which can be analyzed directly in the time domain via distortion. [ABSTRACT FROM AUTHOR]

The reconstruction of the field radiated by a source from square amplitude-only data falls into the realm of phase retrieval. In this paper, we tackle the phase retrieval with two different approaches. The first one is based on a convex optimization problem called PhaseLift. The latter exploits the lifting technique to recast phase retrieval as a linear problem with an increased number of unknowns and then, because the linear problem is highly undetermined, it adds further constraints (based on the mathematical properties of the solution) to estimate it. The second approach formulates phase retrieval as a least squares problem and, therefore, it requires to tackle the minimization of a quartic functional which will be carried out by applying a gradient descent method. In the second part of this paper, in order to corroborate the effectiveness of both approaches, we present the numerical results. Afterward, we provide a comparison between the two methods and finally, we emphasize how the ratio between the number of independent data and the number of unknowns impacts on the performance in both approaches. [ABSTRACT FROM AUTHOR]

In this paper, we present a highly efficient analysis of double-layered stacked gratings that are rotated from each other by any arbitrary angle using the asymptotic corrugations boundary conditions (ACBC) along with classical vector potentials. By casting the resultant system of linear equations into a homogeneous matrix equation, the eigenvalue problem can then be solved, after which the surface-wave dispersion diagram may be generated. In addition to the solutions for modal resonances under sourceless conditions, reflection and transmission analyses of plane-wave incidences constituting source-driven problems are also presented for both normal and oblique incidences. The properties of copolarization and cross-polarization levels in those scenarios are also discussed. The results computed by the code written based on this proposed modal method are compared and validated with those simulated using a commercial full-wave solver. A prototype of the structure was also manufactured and measured. [ABSTRACT FROM AUTHOR]

This paper presents space-time varying (STV) metasurfaces for simultaneously controlling the spatial and temporal spectra of electromagnetic waves. These metasurfaces transform incident electromagnetic waves into specified reflected and transmitted waves, with arbitrary temporal and spatial frequencies. They are synthesized in terms of time-domain generalized sheet transition conditions. Moreover, they are characterized using an analytical method and the unstaggered finite-difference time-domain technique adapted to space-time metasurfaces. STV metasurfaces performing pulse shaping, time reversal, and differentiation are demonstrated as examples. [ABSTRACT FROM AUTHOR]

In near-field scanning, the model parameters for the antenna under test can be determined from measured probe outputs by solving a linear system of equations in the least-squares sense. The model parameters are far-field pattern values, cylindrical or spherical-wave expansion coefficients, or equivalent surface-source values. The normal matrix of this linear system of equations is sometimes extremely ill-conditioned. This occurs when certain sets of model parameters lie outside the spatial bandwidth of the operator that computes the probe output. One remedy is to restrict the sets of model parameters allowed and perform upsampling if needed to achieve the desired accuracy. These ideas are illustrated through analysis and examples that involve both 2-D and 3-D scanning geometries. [ABSTRACT FROM AUTHOR]

A flexible surface integral equation domain decomposition method (SIE-DDM) with reverse operation self-consistent evaluation (ROSE) is proposed to analyze the electromagnetic (EM) scattering by electrically large, multiscale, perfect electrically conducting objects. ROSE is developed for the robust implementation of the Robin transmission condition between adjacent subdomains in SIE-DDM. By interpolating a set of plane waves on the touching faces, small linear systems are constructed, and the entries of the transmission matrix can be solved algebraically. In doing this, direct numerical integration involving complicated geometrical operations over a nonconformal mesh can be avoided. Several numerical results will be presented to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The design of a directional modulation (DM) signal by a phased array is one of the important topics in the field of physical layer security communication. In this paper, we synthesize a sparse array for DM based on convex optimization. The main idea is that a nonconvex optimization problem associated with $\ell _{0}$ -norm is formulated for synthesizing a sparse array. To solve this nonconvex optimization problem, two different solutions are employed to relax the nonconvex optimization problem in a convex way: one is based on iterative reweighted $\ell _{1}$ -norm resulting in a superdirective array, the other is based on mixed integer programming resulting in a nonsuperdirective array. Furthermore, multiple important metrics of a DM transmitter, such as power efficiency, information beamwidth, and dynamic DM signal, are also considered in the optimization problem to achieve better performance of the DM signal via a sparse array. Simulation results show that the proposed synthesis method provides greater flexibility of controlling the security performance, power efficiency, and static or dynamic DM signal while the number of excitations is less than the uniformly spaced linear array in the benchmark problems. [ABSTRACT FROM AUTHOR]

Adaptive process of finite-element method always needs to solve a set of linear systems repeatedly. This communication proposes an accurate and efficient domain decomposition method (DDM) based on a multilevel algorithm and a coarse-level correction strategy. Our developed algorithm facilitates the adaptive refinement process utilizing dynamic coarse-level correction, exploits the hierarchical feature of the refined systems through p-type multigrid method in subdomains, then solves the lowest order system through algebraic multigrid method in auxiliary and node-based spaces. The numerical results show that with this effective coarse-level correction, the residual errors introduced by adaptive refined systems can be eliminated quickly by the DDM. Besides, optimal performance in terms of simulation time is achieved, regardless of workload imbalances during the adaptive steps. Several large-scale electromagnetic problems are analyzed for accuracy as well as performance evaluation of the proposed method. [ABSTRACT FROM AUTHOR]

The second-order wave equation-based discontinuous Galerkin time-domain (DGTD) methods typically employ the first-order absorbing boundary condition for modeling open problems. To improve the modeling accuracy, this paper proposes a novel coupling algorithm of the well-posed perfectly matched layer (PML) for wave equation-based DGTD methods. Based on the domain decomposition technique, the proposed coupling algorithm divides the computational domain into two regions, that is, the physical and PML regions, whose meshes can be nonconformal with each other. Instead of introducing time convolution terms, the new coupling scheme is implemented through employing different DGTD frameworks for the two regions. Specifically, the physical region employs the wave equation-based DGTD framework, while the PML region employs the first-order Maxwell’s curl equations-based DGTD framework. To facilitate modeling of electrically small problems, the implicit Newmark-beta time integration is used for the physical region. To conveniently couple with the physical region, the implicit Crank–Nicolson algorithm is used for the PML region. Numerical results are shown to examine the accuracy and efficiency of the proposed coupling algorithm for modeling electrically small problems. [ABSTRACT FROM AUTHOR]

A fast and simple method for direct electromagnetic scattering problems related to multilayer cylindrical objects having arbitrary shaped dielectric or conducting layers is presented. First, the field in each layer is represented as a series of Bessel and Hankel functions with unknown coefficients. Then, the continuity of the field, along with its radial derivative, is imposed and two equations for several unknowns are obtained for each boundary. By taking the inner products of these equations with complex exponential functions and using the orthogonality property, the equations are augmented to form a linear system for relatively small number of unknown coefficients that can easily be solved. Once these coefficients are determined, one can compute the field value anywhere including the inner regions of the multilayer structure. It has been numerically shown that, for multilayer objects having homogeneous layers and piecewise smooth boundaries, the proposed method is a significantly simple and fast alternative to general purpose numerical techniques. [ABSTRACT FROM PUBLISHER]

A connection between the finite-difference time-domain (FDTD) method and the theory of dissipative systems is established. The FDTD equations for a rectangular region are interpreted as a dynamical system having the magnetic field on the boundary as input and the electric field on the boundary as output. Suitable expressions for the energy stored in the region and the energy absorbed from the boundaries are introduced, and used to show that the FDTD system is dissipative under a generalized Courant-Friedrichs–Lewy condition. Based on the concept of dissipation, a powerful theoretical framework to investigate the stability of FDTD-like methods is devised. The new method makes FDTD stability proofs simpler, more intuitive, and modular. Stability conditions can indeed be given on the individual components (e.g., boundary conditions, meshes, and embedded models) instead of the whole coupled setup. As an example of application, we derive a new subgridding scheme with support for material traverse, arbitrary grid refinement, and guaranteed stability. The method is easy to implement and has a straightforward stability proof. Numerical results confirm its stability, low reflections, and ability to handle material traverse. [ABSTRACT FROM PUBLISHER]

This work is focused on the array thinning problem in shaped beam far-field synthesis. The orthogonal matching pursuit algorithm, which allows finding sparse solutions in linear systems, is combined with a fast full-wave analysis method for antenna arrays based on a spherical wave expansion, thereby taking mutual coupling between real antennas into account in the thinning process. To this aim, the original iterative algorithm is modified so that the current residual is obtained for the selected real coupled antennas in each step of the algorithm. In this way, the remaining nonselected elements are effectively removed instead of turned off. Results for arrays made up of microstrip patch antennas and dielectric resonator antennas arranged in triangular and rectangular lattices are presented. [ABSTRACT FROM PUBLISHER]

An efficient method is proposed for computing electromagnetic wave propagation over lossy terrain profiles using a coupled surface integral equation formulation. The proposed method uses a set of basis functions, which can produce a linear system with much fewer unknowns than that created using pulse basis functions. In addition, the matrix entries can be computed very rapidly using precomputed tabulated values. The method improves upon the original tabulated interaction method (TIM) by extending it to lossy profiles, allowing for back-scatter and by introducing increased accuracy for near-field interactions. The complexity and numerical analysis demonstrates that the proposed method has an extremely low computational complexity and storage requirement. Moreover, the accuracy of the proposed method is demonstrated by comparing the pathloss against numerically precise solutions and measured data. [ABSTRACT FROM PUBLISHER]

We present a domain decomposition (DD) framework for the analysis of impenetrable structures; it allows for the electric field integral equation (EFIE) and combined field integral equation (CFIE), and for open, closed, and open–closed structures. The DD results in an effective preconditioner for large and complex problems exploiting iterative solution and fast factorizations. The DD employs specialized transmission conditions among the domains, and the use of discontinuous Galerkin (DG) allows conformal as well as nonconformal discretizations of domain boundaries; the nonconformal nature of the decomposition gives considerable flexibility in the meshing. The strategy is highly parallelizable, as all the operations involving the subdomains can be performed in parallel. The proposed scheme is implementation independent and can be easily merged with existing electromagnetic codes. [ABSTRACT FROM PUBLISHER]

The electromagnetic dual-primal finite element tearing and interconnecting (FETI-DPEM) method is a nonoverlapping domain decomposition method developed for the finite element analysis of large-scale electromagnetic problems, where the corner edges are globally numbered. This paper presents an extension of the FETI-DPEM2 method, named FETI-full dual primal (FETI-FDP2), where more flexible Robin-type boundary conditions are imposed, on the inner interfaces between subdomains as well as on the corner edges, leading to a new interface problem. Its capacities are tested in the framework of a three-dimensional (3-D) free-space scattering problem, with a scattered field formulation and a computational domain truncated by perfectly mathed layers (PML). First, we compare its accuracy with respect to other FETI-DPEM2 methods and to a complete resolution of the FEM problem, thanks to a direct sparse solver. We show that the convergence of iterative solvers is affected by the presence of the PML and can be accelerated by means of a more accurate approximation, between adjacent subdomains, of the Dirichlet-to-Neumann (DtN) operator. The effectiveness of the iterative solvers are also considered for different test cases. The advantages of the proposed FETI-FDP2 method combined with the associated DtN approximation is numerically demonstrated, regardless the chosen working frequency or the iterative solvers. [ABSTRACT FROM PUBLISHER]

We present simple and stable formulas for computing power (including absorbed/radiated, scattered and extinction power) in current-based volume integral equation formulations. The proposed formulas are given in terms of vector-matrix-vector products of quantities found solely in the associated linear system. In addition to their efficiency, the derived expressions can guarantee the positivity of the computed power. We also discuss the application of Poynting's theorem for the case of sources immersed in dissipative materials. The formulas are validated against results obtained both with analytical and numerical methods for scattering and radiation benchmark cases. [ABSTRACT FROM PUBLISHER]

The sub-domain decomposition iterative method (SDIM) is presented to solve efficiently a large linear system obtained by sampling the boundary integral equations from the method of moments. Then, this new technique is tested on the electromagnetic scattering problem from a large highly conducting one-dimensional rough sea surface. The diagonal blocks are the local impedance matrices corresponding to the geometry sub-domains while the off-diagonal blocks are the coupling matrices describing the interaction between two different sub-domains. The principle of SDIM is to invert the impedance matrix by blocks reducing significantly the complexity in comparison to a direct LU inversion of the whole impedance matrix. In addition, to accelerate the matrix-vector products and to reduce the memory requirement, the adaptive cross approximation (ACA) is applied to compress the sub-domain coupling matrices. For microwave frequencies, the results show that SDIM converges rapidly and faster for the TM polarization. Moreover, the mean compression ratio of ACA is of the order of 98%, which makes this method very efficient. [ABSTRACT FROM PUBLISHER]