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This paper compares three modern and two classical multiobjective optimizers (MOOs) as applied to real-world problems in electromagnetics. The behavior of sophisticated optimizers on simple test functions has been studied exhaustively. In contrast, the algorithms here are tested on practical applications, where the function evaluations are computationally expensive, making the convergence rate a crucial factor. The examples considered include the optimization of a narrowband slot antenna, a mushroom-type electromagnetic bandgap structure, and an ultrawideband Vivaldi antenna. Another popular topic in the literature is in comparing classical MOOs on electromagnetics problems. The modern optimizers chosen in this paper are state of the art and each has a distinct design philosophy. This paper introduces two unique MOOs to the electromagnetics community: BORG, an auto-adaptive genetic algorithm and the Multi-Objective Covariance Matrix Adaptation Evolutionary Strategy (MO-CMA-ES), an extension of the popular single-objective CMA-ES. These algorithms are compared to the Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D), a Chebysheff scalarization algorithm, and two classical MOOs. This paper will study the behavior of these algorithms on problems in electromagnetics with a limited number of function evaluations using five distinct metrics and will provide useful guidelines and recommended optimizer settings. [ABSTRACT FROM AUTHOR]

In this paper, a stable and effective preconditioner for the method of moments-based electric field integral equation matrix, based on the null-field method, is presented to expedite the convergence of Krylov subspace-based fast iterative solution. The preconditioner is computed from all near-field blocks and selected far-field blocks in accordance with the null-field procedure. The final form of the preconditioner is block diagonal, and therefore generates no additional fill-ins in its inverse and is also amenable to parallelization. A complexity analysis is presented to show the near-linear cost of preconditioner construction and usage in terms of computation time and memory. The numerical experiments with a sequential implementation demonstrate on an average 1.5– $3\times $ speed-up in the iterative solution time over threshold-dependent incomplete LU-based preconditioners. [ABSTRACT FROM PUBLISHER]

In this paper, we propose an efficient procedure to obtain loop and star basis functions useful to the surface integral equation. They are of any order, for 3-D curved surfaces, and they keep the solenoidal/nonsolenoidal splitting, improving the performance for low frequencies (near field). These bases, introduced in a former work and applied to the electric field integral equation (EFIE), herein are used in both the magnetic field integral equation (MFIE) and the combined field integral equation (CFIE) providing a good performance even at the low-frequency regime. For addressing the low-frequency performance, scale factors and normalization of the basis are applied to EFIE, MFIE, and CFIE formulations. [ABSTRACT FROM AUTHOR]

A new ramped convergence particle swarm optimization (RCPSO) algorithm to design radio frequency identification (RFID) reader antenna for gain optimization is presented in this paper. The algorithm breaks down the optimization problem by considering only a subset of dimensions at a time, hence overcoming curse of dimensionality. It uses a multi-start approach that alleviates premature convergence. It applies heterogeneous boundary conditions to errant particles. In this paper, the effectiveness of using RCPSO for RFID reader antenna design will be investigated by a number of iterations required to achieve optimum solution along with the quality of solution. RCPSO is built specifically for antenna design. For the microstrip antenna, a significant bandwidth improvement is achieved and the overall antenna dimensions are kept practically the same. The circular gain improves by a significant 2 dBiC over super high frequency (SHF). [ABSTRACT FROM PUBLISHER]

This paper presents an algebraic technique for generating arbitrary-order divergence-conforming bases for curvilinear triangular cells. The bases are constructed by enforcing appropriate constraints on a linear combination of general functions and then extracting the desired bases using singular value decompositions. Koornwinder–Dubiner polynomials are chosen as the general function set. Basic constraints are presented to obtain divergence-conforming bases, and additional constraints are presented to further enforce the bases to be Nédélec. Results from a variety of problems are given to show that the bases exhibit high-order convergence and also produce systems that are relatively well conditioned compared to other basis sets. [ABSTRACT FROM AUTHOR]

Two foremost barriers to the development of fast and efficient simulation algorithms for electromagnetic problems in half-space and planar media are efficient Sommerfeld integral evaluation techniques and fast solvers. In this paper, we focus on challenging these two difficulties in the impedance boundary half-space, which is a proper model for common air-lossy media half-space. Based on the Laplace transformation, we first propose an alternative exact image representation for the Sommerfeld integral in half-space Green’s function. In addition to its fast and absolute convergence property, this new exact image version does not contain any singularities and interprets the Sommerfeld integral as an integral over real image line. Furthermore, this representation allows a rigorous fast multipole expansion (FME), and thus it can be applied to the development of fast multipole solver with controllable precision. However, this exact image representation is not valid for the all Sommerfeld integrals in half-space Green’s function. Therefore, a more generalized single mirror image representation, also exact and computationally efficient, is then presented. The strength of the mirror image is obtained through Weyl’s method and steep descent path approach. Subsequently, an approximated FME scheme for this representation is proposed and studied via numerical examples. We find this approximated FME scheme has a higher accuracy than that of previous work. Numerical results show that the proposed work provides exact and efficient evaluations for Sommerfeld integrals in impedance boundary half-space Green’s function and valuable insights into the development of fast multipole solver for half-space electromagnetic problems. [ABSTRACT FROM AUTHOR]

A new method to improve the accuracy and efficiency of characteristic mode (CM) decomposition for perfectly conducting bodies is presented. The method uses the expansion of the Green dyadic in spherical vector waves. This expansion is utilized in the method-of-moment (MoM) solution of the electric-field integral equation to factorize the real part of the impedance matrix. The factorization is then employed in the computation of CMs, which improves the accuracy as well as the computational speed. An additional benefit is a rapid computation of far fields. The method can easily be integrated into existing MoM solvers. Several structures are investigated, illustrating the improved accuracy and performance of the new method. [ABSTRACT FROM AUTHOR]

For high-power millimeter systems, reflective gratings (RGs) are usually used to control the wave polarization. This paper presents the polarization strategy with two identical RGs. We use the coordinate transformation method for the RG design. A code based on this method is checked by numerical examples and also low-power experiments. Experiments are carried out at frequencies of 60, 70, and 105 GHz. Four gratings are manufactured for test. We present and compare calculated results of the coordinate transformation method with the numerical results of the integral method and low-power test results. The comparison results indicate that the calculation results of the code are accurate and reliable. Finally, the polarization strategy with two identical RGs is studied with the code. Parameters and polarization characteristics including the bandwidth of designed gratings are given. [ABSTRACT FROM AUTHOR]

The nonconformal domain decomposition methods (DDMs) of the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) are presented for computing large electromagnetic scattering/radiation problems. The numerical performance of different transmission conditions between finite element method (FEM) subdomains, and FEM and BI domains is studied in this paper. The Dirichlet transmission condition (DTC) employed at the interface between FEM and BI domains has faster convergence than the Robin-type transmission condition, and this finding is different from the conclusions for the FEM DDMs published in the literature. Furthermore, the cement-element (CE)-based dual-primal finite element tearing and interconnecting (FETI-DP) DDM has faster convergence than the Lagrange-multiplier-based FETI-DP method under the FE-BI system, and is also different from that under the system of the FEM with the absorbing boundary condition (FEM-ABC). It shows that the DDMs of FE-BI-MLFMA have some essential differences from those of FEM-ABC. The analysis of these numerical phenomena is presented in this paper. Further comparison between the DDMs of FE-BI-MLFMA and FEM-ABC demonstrates that the DDMs of FE-BI-MLMFA have essential advantages over those of FEM-ABC. Various numerical experiments confirm the accuracy, efficiency, and flexibility of the nonconformal DDM of FE-BI-MLFMA, which is the CE-based FETI-DP DDM with DTC connecting FEM and BI. [ABSTRACT FROM AUTHOR]

A set of fully numerical algorithms for evaluating the 4-D singular integrals arising from Galerkin surface integral equation methods over conforming quadrilateral meshes is presented. This paper is an extension of DIRECTFN, which was recently developed for the case of triangular patches, utilizing in the same fashion a series of coordinate transformations together with appropriate integration reorderings, and is applicable to coincident, edge adjacent, or vertex adjacent elements. The resulting formulas consist of sufficiently smooth kernels and exhibit several favorable characteristics when compared with the vast majority of the methods currently available. More specifically, they can be applied—without modifications—to the following challenging cases: 1) weakly and strongly singular kernels; 2) basis and testing functions of arbitrary order; 3) planar and curvilinear patches; 4) problem-specific Green functions (e.g., expressed in spectral integral form); and 5) spectral convergence to machine precision. Finally, we show that the overall performance of the fully numerical schemes can be further improved by a judicious choice of the integration order for each dimension. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss a novel technique for sparse array synthesis. The synthesis strategy is based on a sparse-forcing algorithm using an improvement of the reweighted \ell 1 minimization proposed in the framework of the compressed-sensing literature, specifically modified in order to tailor both linear and conformal array synthesis problems. The numerical examples show that the proposed algorithm improves the results provided by concurrent techniques, reducing the number of radiating elements and/or the computational effort. [ABSTRACT FROM AUTHOR]

This paper presents an algebraic method of generating arbitrary-order basis functions suitable for use in moment methods. The basis functions are constructed by enforcing a set of suitable constraints on a more general set of functions, leading to a matrix representation of the constraint condition. The desired bases are then found through use of the singular value decomposition. Divergence-conforming constrained bases are presented for quadrilateral meshes for use in electric and magnetic field integral equations. Appropriate constraints for enforcing normal continuity at cell boundaries are discussed. A variety of problems are analyzed using the constrained bases, and results show that the constrained bases exhibit exponential convergence for smooth structures and produce systems whose condition numbers grow relatively slowly with increasing basis order. [ABSTRACT FROM PUBLISHER]

In this paper, an efficient Laguerre-based body of revolution finite-difference time-domain (BOR-FDTD) method is proposed. A perturbation term and the Gauss–Seidel method are introduced to get the new algorithm. The splitting error caused by the perturbation term can be reduced to a low level by using the iterative method. To be different from its counterpart in the Cartesian coordinate system, the perturbation term used for the off-axis field is not applicable to the field on the axis in the proposed method. On the axis, it is not necessary to add the perturbation term and no nonphysical intermediate variable is involved. No splitting error compensatory term is used for the field on the axis during the iteration. Another difference is that the perturbation term in the proposed method causes a pronounced splitting error on the field point which is close to the axis. Several local iterations near the axis are needed since the splitting error near the axis is especially large. To validate the proposed method, two numerical examples are given. Numerical results show that it obtains a good convergence. Meanwhile, the comparison of the computational expenditure between the proposed method and several other methods indicates its performance. [ABSTRACT FROM PUBLISHER]

Recently, Schelkunoff integrals have been used to formulate a Green’s function for analysis of radiation from a vertical electric dipole over an imperfect ground plane. Schelkunoff integrals were proved to be more suitable for numerical computation for large radial distances than the Sommerfeld integrals which are used conventionally to deal with antennas over an imperfect ground. This is because Schelkunoff integrals have no convergence problem on the tail of the contour of integration, especially when the fields are calculated near the boundary separating the media and for large source–receiver separations. In this paper, the Schelkunoff integrals are utilized to derive a Green’s function for the case of a horizontal electric dipole radiating over an imperfect ground plane (a two-media problem where the lower medium is lossy). A detailed comparison between the presented expressions and the conventional ones based on Sommerfeld integrals is illustrated both numerically and analytically. [ABSTRACT FROM AUTHOR]

In this paper, we report the numerical and experimental observations of electromagnetic or photonic jets created by a planar metallic waveguide filled with dielectric and terminated by an elliptical tip. The theoretical framework of the study is based on the wave concept iterative process (WCIP) method formulated in the spatial domain. The analyzed structure is excited by the fundamental transverse electric mode of the waveguide. The accuracy and efficiency of our program are investigated; the results of the radiated power density show a good agreement compared with those given by finite element method (FEM) simulation. The tangential electric field is computed along the elliptical tip interface and in its vicinity, i.e., in the exterior area. The parameters of the electromagnetic jet phenomenon are investigated according to the geometrical and physical characteristics of the proposed structure. Our numerical simulations are in good agreement with the measurements, indicating that the electromagnetic jet can also be obtained in the microwave field. [ABSTRACT FROM PUBLISHER]

The maximum value of an antenna array’s sidelobe beampattern, or radiation pattern in the power domain, is an important parameter determining its performance. In this paper, when array antenna elements have random phase centers, we approximate the maximum sidelobe value, or peak sidelobe level, as a Gumbel distribution using the extreme value theory (EVT). Before the EVT result, an expression for the beampattern distribution at each angle in the array field of view is found. From this expression, the pointwise convergence of the difference between the beampattern and exponential distributions in the limit of a large number of antennas is obtained. Using the exponential distribution approximation, EVT is applied with samples of the beampattern. A bound is given for the difference between the beampattern sample maximum and its true maximum in the sidelobe region. [ABSTRACT FROM AUTHOR]

In this paper, a guaranteed-convergence method for the accurate and efficient analysis of the electromagnetic scattering by an arbitrarily oriented zero-thickness perfectly electrically conducting (PEC) disk buried in a lossy half-space is presented. An electric field integral equation (EFIE) in the vector Hankel transform domain is obtained by expanding the unknown surface current density in cylindrical harmonics. A convergence of exponential type is achieved by means of Galerkin’s method with expansion functions reconstructing the expected physical behavior of the \bm nth harmonic at the center and the edge of the disk. The obtained coefficient matrix can be quickly computed since its elements can be reviewed as the sum of single integrals efficiently evaluable by means of an analytical acceleration technique and double integrals of exponentially decaying functions. [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]

A triangular dielectric cylinder (dielectric prism) of the size, in cross-section, comparable to or moderately larger than the wavelength is a scatterer, which blends together two different types of electromagnetic behavior: geometrical optics (GO) and resonance. As shown in this paper, the first is responsible, for instance, for enhanced reflection from an isosceles 90° prism, if illuminated from the base. The second is responsible for the peaks in the total scattering and absorption cross-sections (ACSs) at the natural-mode frequencies. The numerical analysis is performed by solving the well-conditioned Muller-type boundary integral equation (IE) discretized using an algorithm with controlled accuracy. [ABSTRACT FROM PUBLISHER]

The efficiency of a method of moments procedure for microstrip antennas is strongly dependent on the convergence of the inverse Fourier transformation (IFT) from the spectral to the spatial domain. This is especially true when considering cylindrical microstrip antennas (CMAs). In the cylindrical case, the calculation of the two-dimensional Green’s functions stays inherently time-consuming. In the planar case, Green’s function can be reduced to a one-dimensional function. The problem, however, becomes a real bottle-neck when probe feeding of a CMA is considered, as the traditional IFT used to calculate the excitation in the spatial domain results in a huge IFT time. In this paper, this problem is explicitly treated. The asymptotical behavior of the probe-related spectral Green’s functions (GFs) is rigorously derived, subtracted, and the corresponding reaction integrals are inverse Fourier transformed without the occurrence of any cylindrical functions. This results in a much improved calculation efficiency for this type of feeding, evident for both thin and thick substrates. Numerical results for CMAs with complex-shaped patches are presented, applicable to both smaller and larger bandwidths. Several structures are fabricated and measurements are in good agreement with simulations. [ABSTRACT FROM PUBLISHER]

In this paper, a mixed inner–outer iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures. The most important novelty of the proposed technique is combining the tangential Poggio–Miller–Chang–Harrington–Wu–Tsai as outer iteration and the electric-magnetic current combined-field integral equation as inner iteration, respectively. In this case, the new method offers the guarantee of high accuracy with faster convergence, especially for electrically dielectric structures in large scale. Furthermore, it presents an excellent compatibility with sparse approximate inverse preconditioning. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the proposed method. [ABSTRACT FROM AUTHOR]

Sparse grid collocation methods are used for uncertainty quantification in electromagnetic propagation problems. The first application here involves waves propagating in lossy media with uncertain permittivities and permeabilities, for which several cases with increasing random-space dimensionality are exemplified. The objective in the second application is to compute expected signal strength above flat Earth surface at ranges far from transmitter location, where randomness is present due to uncertain refractivity of the atmosphere. Two different sparse grid algorithms are demonstrated throughout the paper, and the deterministic evaluators are accessed as a black box by the sparse grid algorithms. The difficult task of a priori method adaption is overcome by a first order check that enforces the black box solver only a few times. Through the results considered, strengths of the two algorithms are differentiated depending on the characteristics of the randomness. The advantage of a new routine used in this work is emphasized by showing its numerical contribution to the field estimation problem in a specific example. By means of the sparse grid methods used, we quantitatively provide the relative importance of each RV in contributing to the changes in the field distribution received at the observation range. [ABSTRACT FROM PUBLISHER]

This paper addresses the convergence of the electric-field integral equation (EFIE)-based matrix systems with the right-hand-side effect. The role of the right-hand-side excitation in determining the convergence rate of the iterative solvers is found to be important or even crucial at low frequencies. The weighted contributions from different singular vectors are decided by not only the corresponding singular values but also the right-hand side. Based on this understanding, we investigate the low-frequency stabilized form of both EFIE and Calderón multiplicative preconditioner EFIE (CMP-EFIE) on capacitive problems. For the parallel-plate capacitor excited by the delta-gap source, the singular vectors with small singular values cannot be excited, and the charge currents on the capacitive surface dominate. Thus, the stability of the EFIE-based system can be achieved at low frequencies. Detailed spectral analysis and convergent results are carried out in order to capture the physical nature of the problems. [ABSTRACT FROM PUBLISHER]

The adaptive cross approximation (ACA) algorithm, when used to accelerate the numerical solution of integral equations for radiation and scattering problems, sometimes suffers from inaccuracies. These inaccuracies occur when the ACA convergence criterion, which is based on an approximation of the residual relative error, is prematurely satisfied. This paper identifies the two sources of this problem and proposes adaptations of the algorithm that remedy them. [ABSTRACT FROM PUBLISHER]

This paper proposes a multigrid preconditioner for integral equation fast analysis of electromagnetic scattering problems. The multigrid model is constructed by recursively dividing every triangular element on the coarse level into 4 small ones. The Rao–Wilton–Glisson (RWG) basis functions defined on the coarse level are expressed with linear combinations of those on the fine level, and the expansion coefficients of which are used to construct the restriction and interpolation operator. To further accelerate the convergence of iterative solution, a set of solenoidal basis functions on the coarse level are constructed additionally, which are also expressed with linear combinations of RWG basis functions on the fine level and adopted to construct the second restriction and interpolation operator. The two sets of coarsening techniques are then combined together to remove the low-frequency components of the iterative error. Numerical results show that the proposed method can reduce both the steps of iteration and CPU time compared with the iterative solver without preconditioning. [ABSTRACT FROM PUBLISHER]

This paper presents a unified framework for solving large-scale multi-region electromagnetic problems using a hybrid conformal/nonconformal domain decomposition method. In this method, an original electrically large problem is first divided into several regions based on its geometry. Each region is then meshed and further decomposed into smaller subdomains. As such, the decomposed problem is mesh-conformal and geometry-conformal within each region but could be mesh-nonconformal and geometry-nonconformal between two neighboring regions. To solve such a problem, a hybrid method is proposed that employs the finite-element tearing and interconnecting (FETI) method to deal with mesh-nonconformal and/or geometry-nonconformal interfaces, where a second-order transmission condition and a crosspoint correction technique are applied to improve the iterative convergence of the interface system and ensure a correct interconnection across subdomain interfaces. For mesh-conformal and geometry-conformal interfaces inside each region, the hybrid method employs the dual-primal finite element tearing and interconnecting (FETI-DP) method to construct an effective coarse grid correction for the interface problem. A unified global system of equations is finally formulated for the interface unknowns from both nonconformal and conformal interfaces. The proposed method is validated with simulation of wave propagation and radiation by broadband antennas and phased-array antennas covered with a radome and a near-field focal lens. [ABSTRACT FROM PUBLISHER]

In this paper a three-dimensional (3-D) numerical technique based on the finite difference frequency domain (FDFD) is implemented to calculate the scattering from arbitrary shaped objects embedded in a continuous random medium. The total field/scattered field (TF/SF) algorithm is integrated with the FDFD to minimize the memory consumption and speed up the calculations. For validation purposes, the radar cross-section of a 2-D conducting cylinder in random medium is calculated using the FDFD technique and compared to previously published data based on the current generator method. An upgrade to a 3-D solver was then inspired once the idea of using the multi-grid technique was introduced to accelerate the convergence rate of the BICGSTAB iterative solver. Thus, allowing the FDFD technique to become a robust method to solve the scattering problem from large targets embedded in random medium. Therefore, using the introduced simulating scheme, one can easily elucidate any scattering information out of real life targets surrounded by random environmental effects. [ABSTRACT FROM PUBLISHER]

This paper describes an algorithm to calculate a large number of roots of the cross-product of Bessel functions and of their first derivatives. The algorithm initially finds the roots of the zeroth order using an auxiliary function that exhibits the same roots as the original cross-products but with better behavior for numerical root search with the Newton–Raphson algorithm. In order to find the roots for higher orders, the algorithm follows a pyramidal scheme using the interlacing property of the cross-product of Bessel functions. The algorithm shows globally convergent behavior for a large range of values of the argument and of the order of the Bessel functions. The roots can be computed to any precision, limited only by the computer implementation, and the convergence is attained in six iterations per root in average, showing a much better performance than previous works for the calculation of these roots. [ABSTRACT FROM AUTHOR]

In computational electromagnetics, the second-kind Fredholm integral equations are known to have very fast iterative convergence but rather poor solution accuracy compared with the first-kind Fredholm integral equations. The error source of the second-kind integral equations can mainly be attributed to the discretization error of the identity operators. In this paper, a scheme is presented to significantly suppress such discretization error by using the Buffa-Christiansen functions as the testing function, leading to much more accurate solutions of the second-kind integral equations, while maintaining their fast convergence properties. Numerical experiments are designed to investigate and demonstrate the accuracy improvement of the second-kind surface integral equations in both perfect electric conductor and dielectric cases by using the presented discretization scheme. [ABSTRACT FROM PUBLISHER]

In this paper, a novel hybrid algorithm based on artificial bee colony (ABC) algorithm and differential evolution (DE) algorithm called ABC-DE is proposed to inherit their advantages and overcome their drawbacks. In ABC-DE algorithm, employed bees employ the mutation and crossover strategies of DE to enforce their exploration ability while onlooker bees keep their original updating strategy to retain the exploitation ability. Classical test functions have been provided to testify the ABC-DE algorithm. Furthermore, ABC-DE is applied to different types of time-modulated arrays (TMAs) pattern synthesis problems, including the syntheses of low equal-ripple sidelobe level (SLL) pattern, deep null level pattern, multiple-beams patterns and satellite footprint pattern. Experiment results reveal that ABC-DE has a promising performance in the convergence rate and the exploration ability when compared with other improved evolutionary algorithms, which indicates that the proposed algorithm can be an effective approach for TMAs synthesis problems. [ABSTRACT FROM PUBLISHER]

This paper considers the solution of the electric field integral equation (EFIE) in electromagnetics. As with associated finite element methods, their solution relies upon the construction of conforming bases. While lowest order (RWG) spaces are near ubiquitous, their extension to higher order offers, potentially, a number of benefits in terms of accuracy and efficiency, which has been well documented in both finite elements and integral equation formulations. A further evolution of higher order conforming bases is the hierarchical basis. These have demonstrated considerable gains in efficiency in finite element applications. Such bases allow for the development of effective acceleration schemes, for instance, the multilevel Schwarz type preconditioner (p-MUS). An obvious question arises as to the applicability of such hierarchical bases and their associated acceleration schemes to integral equations. It is seen that the conclusions as to their efficacy depend strongly on the scattering regime. In particular, high-frequency problems (those where the wavelength is the principal determinant of mesh size) are shown to benefit little from hierarchical functions. On the other hand, for “low-frequency” problems (where geometry is the main determinant of mesh size), there are significant improvements in performance over corresponding interpolatory schemes. [ABSTRACT FROM PUBLISHER]

This paper introduces the use of the quasi 3-D mixed potential integral equation formulation for structures with a periodicity in two dimensions. The quasi 3-D formulation allows to use both horizontal and vertical conductors, and dielectric inclusions. The key innovation is the use of an effective algorithm to calculate Periodic Green's Functions (PGFs) for vertical currents in the planar multilayered background medium. This algorithm retains the same scheme as for a single source Green's Function (GF). In both cases, the GFs are calculated via an inverse Fourier transform of the GFs in the spectral domain, which are known in closed form. In order to remedy the poor convergence for small source—observation distances, an asymptotic extraction is used, yielding a very compact algorithm, and acceleration techniques are applied. Simple guidelines are proposed to construct asymptotes having the required leading terms and a good convergence. It is shown that many acceleration algorithms widely used in literature are actually able to perform well only in specific circumstances. As far as the authors can see, there is still no general and robust technique, yielding highly accurate results under all circumstances. Several examples illustrate the efficiency of the technique. [ABSTRACT FROM AUTHOR]

Existing Green functions for a conducting wedge in the form of infinite series of orthogonal eigenfunctions are known to suffer from slow and conditional convergence 1) near the source point, due to the singularity of the Green functions at source points, and 2) when the source point is near the surface of the wedge, due to the presence of a nearby image source. As a result, such expansions are unsuited for the exact solution of singular integral equations wherein values of the Green functions at the source point do appear inside the integral. In this paper, alternative expansions are proposed which converge rapidly for any combination of the source and observation points. The main idea is to extract in closed form both the singular term and the nearby image term together with certain simple asymptotic terms. This helps isolate the inherent singularities and, thus, transform the remaining part of the Green function into a rapidly converging series of elementary terms. Numerical examples and case studies illustrate the stability and high accuracy of the new expansions. Application to the solution of an integral equation associated with wave diffraction by perfectly conducting curved strips in the vicinity of a wedge is exemplified. [ABSTRACT FROM PUBLISHER]

In this paper we propose an efficient and accurate iterative numerical approach to analyze EM scattering from 1-D dielectric rough surfaces. It is based on a new splitting of the impedance matrix Z to improve the asymptotic convergence rate of the resultant iterative system. The structure of split matrix is then fully explored, in combination with the application of an identity for inverse of block matrix, to further reduce the computational and storage complexity. The embedded matrix-vector product is computed using the spectral acceleration technique. Extensive numerical simulations demonstrate a couple of appealing features of this proposed method for Gaussian surface with Gaussian spectrum: 1) It converges faster than both forward-backward method (FBM) and FBM with spectral acceleration (FBM-SA); 2) For HH polarization, the proposed method is about twice as fast as FBM-SA. For VV polarization, the proposed method is better when the rms slope is not larger than 16^\circ or interestingly when rms height is beyond 2.0 wavelengths. Moreover, it converges for cases where FBM-SA fails for both polarizations. These features indicate that the proposed method can be effectively used to analyze EM scattering from 1-D dielectric Gaussian surface with Gaussian spectrum. [ABSTRACT FROM AUTHOR]

A nonstandard Schwarz domain decomposition method is proposed as finite-element mesh truncation for the analysis of infinite arrays. The proposed methodology provides an (asymptotic) numerically exact radiation condition regardless of the distance to the sources of the problem and without disturbing the original sparsity of the finite-element matrices. Furthermore, it works as a multi Floquet mode (propagating and evanescent) absorbing boundary condition. Numerical results illustrating main features of the proposed methodology are shown. [ABSTRACT FROM AUTHOR]

Methods employing auxiliary sources are applied to electromagnetic scattering problems by 2-D noncircular scatterers. Specific cases are considered for which the singularities of the analytic continuation of the scattered field into the interior of the scatterer can be analytically determined. Then, it is shown that the amplitudes (currents) of the sources diverge and oscillate when the auxiliary curve does not enclose these singularities. Still, the electric fields computed by means of the divergent and oscillatory currents are convergent and correct. The correctness of the computed fields is validated by comparison with the exact solutions (where possible) as well as with the numerical solutions computed via commercial field simulation software. [ABSTRACT FROM AUTHOR]

Low-order subdomain basis methods of moments provide little help when highly accurate electromagnetic computations are required. High order modeling, on the other hand, can fill the need for enhanced accuracy but at the expense of greater implementation cost. To supplement such methods, this paper presents Nyström techniques, both easily implemented and highly accurate, relevant to TM scattering by arbitrarily shaped smooth infinite curved strips. The analysis takes full account of both the singular nature of the kernels and the singularities of the solution at the edges; as a result, the proposed solutions are exponentially converging. In addition, by eliminating inner product integrals, closed form analytical expressions are obtained for all matrix elements; thus our algorithms have very low implementation and computational cost. Detailed numerical examples and case studies amply demonstrate the efficiency, stability, and extremely high accuracy of the algorithms. These algorithms apply uniformly from electrically small to electrically large conducting screens. With only slight modifications the present analysis can be also used to obtain exponentially converging Galerkin solutions. [ABSTRACT FROM PUBLISHER]

In this paper, a volume integral equation (VIE)-based modeling method suitable for a patch or slot antenna on a thin finite dielectric substrate is developed and tested. Two new key features of the method are the use of proper dielectric basis functions and proper VIE conditioning, close to the metal surface, where the surface boundary condition of the zero tangential E -component must be extended into adjacent tetrahedra. The extended boundary condition is the exact result for the piecewise-constant dielectric basis functions. The latter operation allows one to achieve a good accuracy with one layer of tetrahedra for a thin dielectric substrate and thereby greatly reduces computational cost. The use of low-order basis functions also implies the use of low-order integration schemes and faster filling of the impedance matrix. For some common patch/slot antennas, the VIE-based modeling approach is found to give an error of about 1% or less in the resonant frequency for one-layer tetrahedral meshes with a relatively small number of unknowns. This error is obtained by comparison with fine finite-element method (FEM) simulations, or with measurements, or with the analytical mode matching approach. Hence it is competitive with both the method of moments surface integral equation approach and with the FEM approach for the printed antennas on thin dielectric substrates. [ABSTRACT FROM AUTHOR]

A Green’s function technique is developed for the full-wave analysis of a loop excited conical horn, considering all excited modes. The technique avoids the need for discretization of the horn antenna structure into several cascaded sections or the imposition of unknown currents over the entire horn surface, thus reducing the computational burden significantly. The aperture fields of the conical horn are investigated for varying horn lengths. Reflection effects at the aperture is found to be minimal for horn lengths over $5\lambda $ , corresponding to a horn aperture diameter of more than $2\lambda $. Analytical expressions used to represent the aperture fields over the conical cap at the aperture are provided from which the radiation fields are derived to characterize the aperture radiation. It is observed that the loop excitation can be appropriately located relative to the horn apex to couple to appropriate modes to generate broadside or monopole-like pattern characteristics. Also, in addition to the simplicity of the feed configuration, the loop position can be properly selected to couple to multiple modes that has a significant impact on the pattern directivity and sidelobe levels. The developed technique is also used to rigorously evaluate and characterize the contribution of each mode at resonance. [ABSTRACT FROM AUTHOR]

The applicability of the alternating-direction-implicit (ADI) iterative method for the 2-D finite-difference frequency-domain (FDFD) solution of electromagnetic problems is studied, evaluated, and optimized. The ADI is used as an iterative solver of the system of linear equations resulting from the FDFD formulation. The physical limitations of applying the ADI method with a single acceleration parameter are examined in terms of its convergence behavior. In order to overcome these limitations, multiple acceleration parameters are necessary. An optimization procedure based on the simulated annealing algorithm is presented in order to obtain the optimum or near-optimum acceleration parameters. The approach is applied on the scattering problem by a dielectric cylinder as a test. The optimized acceleration parameters are compared with the ones suggested by Hadley. The acceleration parameters depend on the type of transparency conditions used to treat open-boundary problems. A simple absorbing layer (ABL), the stretched-coordinated perfectly matched layer (SC-PML), and the uniaxial PML are tested for both TE and TM polarizations. The SC-PML absorbing condition seems to be the best solution for the ADI iterative implementation of FDFD. Finally, empirical acceleration parameters are proposed for arbitrary scatterers for ABL and SC-PML absorbing conditions. [ABSTRACT FROM PUBLISHER]

A method is explored and developed for significantly accelerating the computation of the Ewald series representation for periodic homogeneous media Green’s functions. The method involves extracting corner singularity terms from the corners of the unit cell, resulting in a smooth regularized Green’s function that is amenable to interpolation. The approach can be used to accelerate layered-media problems, where application of Kummer’s method splits the spectral (Floquet modal) series representation into a rapidly converging difference series that is regular plus a residual series that contains any spatial singularities present. The residual series corresponds to a homogeneous medium, and can thus be treated with the method proposed here. [ABSTRACT FROM PUBLISHER]

The Ewald method for evaluating the free-space 1-D periodic Green’s function is extended to leaky waves by allowing for complex wavenumbers. It is shown that care must be taken when choosing the path of integration in the complex plane in the derivation of the Ewald method in order to obtain solutions that correspond to physical leaky-wave solutions. The use of different paths results in an evaluation of the Ewald method using an analytical continuation of the exponential integral function previously used when the wavenumber is real. The extension of the Ewald method to complex wavenumbers allows for the treatment of practical periodic leaky-wave antennas and periodic guiding structures with losses, as well as metamaterials, including 1-D chains of plasmonic nanoparticles. [ABSTRACT FROM PUBLISHER]

The late-time evaluation of electromagnetic (EM) field quantities yielded by convolution integrals that combine Green’s functions available at discrete time samples and strictly causal excitations is critically revisited. A typical situation is used for tracing the causes of the divergent late-time behavior that is often experienced. A framework combining a suitable integral partitioning with a polynomial approximation is shown to effectively guarantee the integrals’ convergence. The formulation is validated via numerical experiments evidencing its accuracy and computational efficacy. The method is amenable to be used in a wide range of problems requiring the late-time evaluation of convolution integrals of the indicated type. [ABSTRACT FROM AUTHOR]

The necessity of conforming testing procedures in developing accurate and reliable surface-integral-equation-based solvers for homogeneous penetrable objects is demonstrated. It is shown that only in Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) formulation with a conforming testing procedure, the interface conditions become properly tested for both the tangential and normal field components. Numerical experiments illustrate that the use of a nonconforming testing procedure can lead to a significant decrease on the solution accuracy or erroneous diverging results. [ABSTRACT FROM PUBLISHER]

For high-volume manufacturing, yield estimation is an important design step to determine the effects of uncertainties in the fabrication process. The tolerances associated with the fabrication process are applied to the statistically significant system parameters, and a Monte Carlo (MC) simulation is historically done to accurately estimate the yield. This process becomes computationally very expensive when the number of statistically significant system parameters are either too difficult to intuitively determine or are too high. A nonlinear partial-least-squares-based polynomial chaos expansion (NLPLSs-based PCE) is proposed as a solution for complex antenna yield analysis. NLPLS-based PCE effectively reduces the system dimensionality using NLPLS and simultaneously extracts the statistical information on the same sample set, that is, yield, using PCE. It is also possible to perform a global sensitivity analysis using NLPLS-based PCE surrogates, providing an additional advantage. This method is illustrated using an eight-variable single-frequency patch antenna, an eight-variable dual-band patch antenna, and a 37-variable diplexer requiring 30, 10, and 30 analysis points, respectively, to obtain converged yield estimates. [ABSTRACT FROM AUTHOR]

In this article, we present a data-free method to solve differential equation using artificial neural networks (ANN). This method exploits the universal function approximation nature of a neural network to mimic a specified partial differential equation (PDE) and provide its solution. Specifically, use of simple feed-forward artificial neural network (FF-ANN) is shown to demonstrate the solution of 1-D second-order differential equations without use of any prior data. The article also demonstrates that the similarity in two PDEs is akin to similarity in the optimized weight matrices attained after the solution using FF-ANN. This property is then utilized for a transferred learning to enable faster convergence of a new PDE, based on the prior solution of a similar PDE. The concept is shown while considering a general form of second-order PDE, and considering specific cases of scalar in-homogeneous wave equation form and Poisson Equation form. Error convergence below 10−6 is shown and the transferred learning process shows typical time acceleration by a factor of 1.5–3 for the considered equations. [ABSTRACT FROM AUTHOR]

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]

A volume integral equation formulation for the equivalent current is investigated by decomposing the L_2-conforming unknown current into orthogonal functions. The decomposition shows that the solenoidal, irrotational and harmonic subspaces scale differently with respect to the material parameter. This has a negative effect on the conditioning of the system, and thus, the convergence of the iterative solution slows down with increasing permittivity. We construct discrete decomposition operators, and use them as a preconditioner for the electric current volume integral equation. The eigenvalues of the resulting system are almost independent on the permittivity. Numerical examples show that the proposed preconditioner improves the condition number and decreases the number of iterations required to solve the system. However, efficient evaluations of the projection operators require additional regularization techniques such as algebraic multigrid preconditioners. [ABSTRACT FROM PUBLISHER]

A novel, real-time, two-dimensional method to find the shape of a body from its scattered electric fields is presented. The method is based on a unique combination of the information obtained from the target using the SAR formulation with a novel fast model-based inversion. In the first step, a fast implementation of the SAR inversion is used to recover an initial estimate of the body shape. Secondly, the phase and amplitude of the SAR image are used to extract a set of first guess contours close to the actual position of the body under test. In a third step, these contours are used as a starting point for a model-based inversion in order to disregard the contours that do not match the body profile and to improve the final result. Resolution of less than half of a wavelength for the proposed method is achieved using representative simulation results and measured data. [ABSTRACT FROM PUBLISHER]

In this article, a fast high-order volume surface integral equation (HOVSIE) formulas solver will be presented to fast calculate the wideband electromagnetic (EM) scattering of anisotropic medium-metallic composite objects. First, in the HOVSIE, the equivalence volume and surface current vectors are discretized by the high-order hierarchical vector basis functions (HVBFs), which can reduce unknowns and facilitate the calculation of the broadband EM scattering. Second, a fast wideband algorithm, i.e., the hybrid multilevel accelerated Cartesian expansion–multilevel fast multipole algorithm (MLACE-MLFMA), is integrated to accelerate the matrix-vector multiplication in the iterative solution. Finally, in order to improve the iterative convergence, a simple overlapping domain decomposition method (ODDM)-based preconditioner is also employed in the proposed HOVSIE enhanced by the MLACE-MLFMA. Summarily, three advantages can be found here: 1) more flexible calculation of the wideband EM scattering; 2) less memory occupation; and 3) better iterative convergence. The accuracy, efficiency, and flexibility will be demonstrated in the numerical examples. [ABSTRACT FROM AUTHOR]