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In this work, we propose simple and efficient tridiagonal computed sparse preconditioners for improving the condition number for large compressed electric field integral equation (EFIE) method of moment (MoM) matrix. The preconditioner computation is based on the triangle and block triangle interaction and filled tridiagonally. The computed preconditioner is highly sparse and retains the ${O(N)}$ complexity of computation and preconditioner matrix solution time. Numerical results show the efficiency and accuracy of the proposed preconditioner. [ABSTRACT FROM AUTHOR]

The Rao–Wilton–Glisson (RWG) basis function (BF)-related convolutional surface integrals are intrinsically 2-D. The Schaubert–Wilton–Glisson (SWG) BF-related convolutional volume integrals are 3-D in nature. It has been shown that such integrals can be reduced to a summation of several 1-D integrals by repeatedly applying the divergence theorem. To the best of our knowledge, there are no known analytic formulas for the 1-D integrals, and consequently, one must choose a quadrature rule to get the final results. The 1-D integrals are prone to numerical errors when the observation point is close to the source. We propose that sinh-related transformations can be used to improve the accuracy, which has been shown to have exponential convergence with respect to the number of Gauss–Legendre quadrature points in the numerical examples. We can reach ten or more significant digits in the convolutional integrals pertinent to RWG or SWG functions with a small number of quadrature points. [ABSTRACT FROM AUTHOR]

In the solution of frequency- and time-domain integral equations, the singularity cancellation transformations are well-known for the treatments of the singular integrals involving Green’s functions and their gradients. The cancellation transformations for strongly near-singular integrals become inaccurate and inefficient for an extremely deformed triangular patch, and this phenomenon is referred to as shape-dependent problem in this article. As the degree of the singularity increases, the shape-dependent problem of strong near-singularity is more severe than that of the weakly near-singular integrals. Furthermore, if the source triangle is deformed, the accuracy of the cancellation methods decreases when no near singularity exists. In this work, we first investigate the reason for these problems via the theoretical analysis with numerical verification. Second, an updated framework of singularity cancellation methods for strongly near-singular integrals is proposed, which has a fast and consistent convergence rate for both regular and irregular triangles. Third, some numerical experiments are presented to illustrate the effectiveness of the theoretical framework and the proposed transformations. [ABSTRACT FROM AUTHOR]

The singularity cancellation transformations are well-known for calculating weakly singular and near-singular integrals in integral equation solutions. However, some singularity cancellation methods suffer from the shape-dependent problem of inaccuracy and inefficiency for deformed triangles. By the theoretical analysis and numerical verification in this article, the relation between the near-singularity and shape-dependence of the singularity cancellation schemes is discussed. Moreover, a novel framework for devising cancellation transformations of weakly near-singular integrals is presented, which results in fast convergence for both regular and irregular triangular domains. Some numerical results are given to illustrate the validity of the theoretical framework and the efficiency of the proposed transformations. [ABSTRACT FROM AUTHOR]

The combined-field integral equation (CFIE) usually is less accurate than the electric-field integral equation (EFIE), especially for objects with sharp edges and corners. In this work, we propose a simple but accuracy enhanced CFIE (AE-CFIE) strategy for computing scattering from perfect electric conductor (PEC) objects. AE-CFIE directly replaces the original CFIE on the sharp edges with EFIE. Using the dihedral angle of the meshes to describe the sharpness of the geometric structure, the hybrid criterion of EFIE/CFIE has been studied in detail. This strategy can be implemented conveniently under exiting basis functions and only a few lines of code need to be changed. Due to the inclusion of EFIE, AE-CFIE may sacrifice the convergence speed compared with CFIE. Therefore, we also investigate the performance of AE-CFIE with or without the preconditioner. Numerical examples show the performance of AE-CFIE, and a comprehensively study is made to demonstrate its validity, reliability, and stability. [ABSTRACT FROM AUTHOR]

With the development of electromagnetic theory and microwave engineering, researchers have proposed many novel quasi-periodic arrays to realize various functions in controlling electromagnetic wave propagation. They have similar elements located on the periodic lattices. Full-wave simulation of the quasi-periodic arrays is necessary and challenging, because the whole array is usually electrically large and multiscale. In this communication, we study a fast algorithm for the full-wave modeling of the quasi-periodic arrays. It constructs a reduced basis set based on the geometric similarities among the array elements. Then, we use linear projection to “recover” periodicity numerically so that the fast Fourier transform can be used to accelerate the computation of the whole array. The computational complexity of this algorithm is $O(N\text {log}N)$ , where $N$ is the number of elements in the array. Numerical examples verify its potential in solving large-scale quasi-periodic arrays. [ABSTRACT FROM AUTHOR]

Recent work on developing novel integral equation formulations has involved using potentials as opposed to fields as unknown variables. This is a consequence of additional flexibility offered by potentials that enable development of well-conditioned systems. Until recently, most of the work in this area focused on formulations for analysis of scattering perfectly conducting objects. In this paper, we present well-conditioned decoupled potential integral equations (DPIEs) formulated for electromagnetic scattering from homogeneous dielectric objects. The formulation is based on decoupled boundary conditions derived for scalar and vector potentials. The resulting DPIE is a second kind integral equation, and does not suffer from either low frequency or dense mesh breakdown. Analytical properties of the DPIE are studied for spherical systems, and results provided demonstrate well-conditioned nature (and bounded spectrum) of the resulting linear system. [ABSTRACT FROM AUTHOR]

The translation matrix ($T$ -matrix) solution to the 3-D problem of scattering of the electromagnetic waves from a dielectric layered medium with random rough interfaces is presented. The solution is based on the coupled vector integral equation of the electric field using the dyadic periodic Green’s function as a kernel. It is shown that the $T$ -matrix solution conserves energy, the bistatic scattering pattern is regular even in cases, where guided modes within the layered medium are excited, and also that the method’s results coincide with those of the second-order Small Perturbation Method (SPM2) in the small height limit. One of the advantages of the $T$ -matrix method compared to the SPM2 is the wide validity range of the solution, which is also studied. [ABSTRACT FROM AUTHOR]

In this paper, we report the complex resonant frequencies of inhomogeneous anisotropic spherical resonators. The anisotropy can be of gyroelectric or gyromagnetic type, having one isotropic axis. Two kinds of configurations are considered: an anisotropic sphere and an anisotropic spherical shell coating a concentric perfect electric conducting core. Two full-wave methods are employed for the calculation and verification of the resonances. The first is a method based on the weak form of the coupled-field surface-volume integral equation (CFSVIE), which is solved using entire domain basis functions of Dini-type. The second is the discrete eigenfunction method (DEM) that allows the expansion of the unknown fields in the region of anisotropy in terms of spherical vector wave functions. Both the CFSVIE and the DEM are validated by comparisons with separation of variables method, regarding isotropic and metallic-isotropic resonators. It is shown that commercial packages, such as HFSS, cannot address the full spectrum of such open structures. Numerical results for complex resonances, verified by both the CFSVIE and the DEM, are given for various anisotropic configurations. Finally, magnetic plasmon resonances are particularly examined in ferromagnetic resonators. [ABSTRACT FROM AUTHOR]

Implementation of max-ortho basis functions is proposed in a method for analysis of axially symmetric metallic antennas based on exact kernel of electric field integral equation in combination with Galerkin testing. High-precision evaluation of matrix elements is enabled by: a) representing them as a linear combination of impedance integrals due to the Legendre polynomials and their first derivatives; b) using the singularity cancelation techniques; and c) evaluating the Legendre polynomials and their first derivatives by well-known recurrent formulas. Applicability of max-ortho bases up to expansion order of $n =128$ is illustrated on a full-wave thick dipole antenna. [ABSTRACT FROM AUTHOR]

In this paper, we propose a potential-based integral equation solver for low-frequency electromagnetic (EM) problems. In this formulation, the scalar potential ( \Phi ) equation is solved in tandem with the vector potential ( \textbf {A} ) equation. The resulting system is immune to low-frequency catastrophe and accurate in capturing the electrostatic and magnetostatic physics. The fast convergence of the new \textbf {A}$ - $\Phi $ system, which is a typical symmetric saddle point problem, is made possible through the design of an appropriate left constraint preconditioner. Numerical examples validate the efficiency and stability of the novel formulation in solving both EM scattering and circuit problems over a wide frequency range up to very low frequencies. [ABSTRACT FROM PUBLISHER]

Electromagnetic scattering by super-thin conducting objects is formulated by integral equation approach. It could be difficult to obtain accurate solutions for such a problem because the current density changes dramatically near the edges of such objects and many low-quality meshes exist on the side faces of objects when discretized. Traditionally, the electric field integral equation is used to describe the problem and the three-dimensional (3-D) objects are approximated as a two-dimensional (2-D) open structure with a summation of the current density at two opposite sides. In this communication, the magnetic field integral equation (MFIE) is employed to govern the problem and the super-thin objects are strictly treated as 3-D objects. The MFIE is a second-kind integral equation resulting in a better conditioning and can also release the low-frequency breakdown problem, but it has not been applied to very thin structures. In the method of moments solution, a robust near-singularity treatment for its kernel is developed based on the Green’s lemma. The derived formulations are friendly and very suitable for low-quality triangular meshes. Numerical examples are presented to demonstrate the scheme and good results have been obtained. [ABSTRACT FROM PUBLISHER]

An iterative-based hybrid method, which combines the volume-surface integral equation (VSIE) and the modified surface integration (MSI) method, is presented to analyze the radome-enclosed antennas in receiving mode. Compared with the previously published hybrid approaches, this method improves computational accuracy by including the effects of shaded wall of the radome and the mutual interactions between antennas and radome during the numerical solution of the VSIE in an iterative manner. By embedding different parts of the antenna-radome structure (ARS) into three distinct oct-trees, the multilevel fast multipole algorithm (MLFMA) is used to accelerate both the VSIE solution and the surface/volume integrations in the MSI stage. The new method obtains more accurate results than its original version within less CPU time, and keeps good accuracy with much less memory usage and computational time when compared with the MLFMA-accelerated full-wave VSIE solution for the entire ARS. [ABSTRACT FROM PUBLISHER]

In this paper, the mixed-order stabilized biconjugate gradient fast Fourier transform (mixed-order BCGS-FFT) method is presented to solve the scattering problem of magnetodielectric materials with general anisotropy in layered media. While the volumetric roof-top functions are used as the testing functions for the coupled field volume integral equation and the basis functions for flux densities, the second-order curl conforming basis functions are applied to expand the vector potentials with the aim of both preserving the continuity of their tangential components and avoiding the zero terms that might otherwise be caused by the divergence operator. The layered medium Green’s function (LMGF) is efficiently evaluated through the recursive matrix method along with an interpolation technique. Several numerical experiments are presented to demonstrate the high accuracy and efficiency of the method. Different from the previously published works that aim to solve the similar problem, the new contribution of this work is to extend the mixed-order BCGS-FFT method to accommodate the layered background medium. Therefore, the 3-D FFT acceleration for integral kernels associated with the LMGF as well as the interpolation technique has been implemented and combined with the mixed-order BCGS-FFT method. [ABSTRACT FROM PUBLISHER]

A nested complex source beam (NCSB) method based on octree structure is proposed to accelerate the method-of-moments (MoM) solution for three-dimensional (3-D) electromagnetic scattering analysis. At the finest level, the far-field contribution of each basis function is expressed with that of complex source beams (CSBs) distributed on the equivalent sphere surface for every group. Furthermore, the far field radiated by CSBs of the source group at child level can be represented by that radiated by CSBs of the source group at parent level. Similarly, the received field of CSBs for each observation group at the parent level can be expressed with that of CSBs belong to their child level group. An equivalent relationship of CSBs between every two adjacent levels is built to obtain the nested equivalent process for NCSB method, and only the CSBs at the finest level have the direct association with the basis functions in their group. The NCSB method is shown to be O(NlogN) computational complexity for both matrix–vector product (MVP) time and memory storage by numerical examples with appropriate parameters, and numerical results demonstrate the better efficiency of the proposed method than the current multilevel CSB method. [ABSTRACT FROM PUBLISHER]

The scattering problem from an object coated with materials is solved in the frequency domain. The coating is modeled by an impedance boundary condition (IBC) implemented in an integral equation (IE) prescribed on its outer surface. The Leontovich IBC (IBC0) is local and constitutes a poor approximation for low index coatings. A possible remedy is to employ higher order IBCs. These, as well as the IBC0, are implemented in two IE formulations: 1) CFIE with the electric current as sole unknown and 2) EFIE+MFIE where the unknowns are both the electric and magnetic currents. The problems raised by the discretization of the surface div and surface curl operators involved in the IE and IBC formulations are solved by employing a simple and computationally cheap technique, the accuracy of which is numerically assessed. The performances of the various IBC and IE formulations are evaluated by calculating the radar cross section (RCS) of some axisymmetric objects. [ABSTRACT FROM PUBLISHER]

Periodic metamaterial unit cells are analyzed by using inhomogeneous plane wave scattering. The complex modes of the unit cell are derived using either the poles or the zeroes of the complex reflection coefficient of the fundamental Floquet mode. The required reflection coefficients are computed by a doubly periodic finite element boundary integral technique. The search for the eigenvalues is accelerated by the nonlinear Nelder–Mead method. Usually, pairs of eigenvalues are observed, which can be both, real or conjugate complex. Also, the eigenvalues correspond either to proper or improper modes. By selecting the proper or the improper modes during field computation, the other type of modes is removed from the observed response and, instead, zeroes are found in the reflection coefficient. This can explain the absorption behavior of single-sided open periodic leaky structures by investigating their reflection coefficient with the proposed inhomogeneous plane wave excitation approach. The obtained results for various single-sided open periodic unit cells are in good agreement with the results of other methods, where in the presented excitation based method there is no need to solve any dispersion equation in the complex plane. [ABSTRACT FROM PUBLISHER]

An efficient approach that combines the coupled volume surface integral equation (VSIE) accelerated by multilevel fast multipole algorithm (MLFMA) and the modified surface integration (MSI) method is proposed to analyze the antenna-radome structures (ARS) in receiving mode. The hybrid method not only reduces the computational time and memory requirement as compared to the purely full-wave solutions, but also more importantly overcomes the difficulties in conventional high-frequency approximate methods for analyzing the properties of the radome-enclosed receiving antennas or arrays. Numerical results are shown to illustrate the validity, efficiency, and accuracy of the proposed method. [ABSTRACT FROM PUBLISHER]

An efficient methodology is introduced for rapid analysis and design of three-dimensional (3-D) doubly periodic structures over a wide frequency range based on hybrid finite element boundary integral (FEBI) methods. The 3-D doubly periodic structures can be represented as nonorthogonal lattices composed of general inhomogeneous bianisotropic media with arbitrarily-shaped metallic patches. Based on Floquet theory and periodic boundary conditions, the original stated problem that involves infinite periodic structures can be converted into a single unit cell. Using the equivalence principle, the derived BI equation formulation is applied to the top and bottom surfaces of the unit cell, which results in a perfectly reflectionless boundary condition for the FE-based approach. Then, the unit cell was meshed using triangular prismatic volume elements, which provide a great deal of flexibility in modeling complex planar geometries with arbitrary shapes in the transverse direction. The adaptive integral method (AIM) was employed to accelerate the calculation of the matrix-vector product for the BI portion within the iterative solver. Furthermore, a model-based parameter estimation (MBPE) technique was proposed for the wide-band interpolation of the required impedance matrix elements in the BI part for near field components that were used in the AIM procedure. The accuracy and efficiency of the proposed hybrid algorithms are demonstrated by the presented numerical results (e.g., in comparison with analytical solutions). Several simulation results are presented to illustrate the flexibility of the proposed methods for analysis of frequency selective surfaces with arbitrarily-shaped metallic patches, bianisotropic materials, and nonorthogonal lattice configurations. [ABSTRACT FROM PUBLISHER]