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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]

Solving electromagnetic (EM) problems with thin conducting objects by integral equation approach could encounter some unfavorable factors. The individual electric field integral equation (EFIE) and magnetic field integral equation (MFIE) may deteriorate the conditioning of matrix equations due to their degeneration when the thickness reduces. Also, there are more evaluations of near-singular integrals in filling the impedance matrix because the near interactions between observation points and source patches are common. In addition, many triangular meshes could have a high aspect ratio owing to the small thickness and this will present a difficulty for the accurate evaluation of self- and near-interaction elements. Aiming to these factors, we use the combined field integral equation (CFIE) as a governing equation and develop an efficient Nyström solver for the problems based on a singularity treatment technique without subdividing triangular patches. Typical numerical examples are presented to demonstrate its robustness. [ABSTRACT FROM PUBLISHER]

For the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous 3-D objects, a previously published one-way domain decomposition method (DDM) is considered: the computational domain is partitioned into concentric subdomains on the interfaces of which Robin-type transmission conditions (TCs) are prescribed, with an integral equation (IE) on the outer boundary of the computational domain (DDM-IE). On account of the large computing time required by the solution of the isolated IE system, in this paper the IE is replaced by the integral representations (IRs) of the fields that requires only a few matrix-vector products (adaptive absorbing boundary condition: AABC). The IRs necessitate the calculation of the electric and magnetic currents on some inner surface S that is chosen to be the interface between the last two subdomains. Taking advantage of the TCs, the unknown current on S (here the magnetic current) is obtained via a change of bases H(rot) to H(div) that allows the accurate computation of the IR integrals involving the surface divergence terms, and permits the separate solution of the FE systems in the last two subdomains. The matrix-vector products in the AABC are performed only once per DDM iteration. Numerical results are presented that illustrate the accuracy of the DDM-AABC and its superiority, in terms of computing time, over the DDM-IE. Also, some indications are given on how to estimate numerically the convergence rate of the DDM-AABC. [ABSTRACT FROM AUTHOR]

Using the recently developed method based on the rigorous theory of singular and hypersingular integral equations (IEs) and Nystrom-type discretization, a paraboloidal reflector assisted with a conical shield is investigated. To decrease the computation time we propose a new method of calculation of the Modal Green's Functions in the quasi-optical range. The far and near fields of the studied reflector are analyzed in the transmission and reception cases, and reveal fine features that escape asymptotic analysis. Elementary numerical optimization of the shield-assisted paraboloidal antenna is performed. [ABSTRACT FROM AUTHOR]

Numerical solutions for electromagnetic (EM) integral equations rely on the discretization of integral domains and the use of meshes for geometric description. Meshing geometries is very tedious, especially for complicated structures with many details (tiny parts) and geometric discontinuities (corners or edges), and remeshing could be required in many scenarios. To reduce the costs of generating quality meshes, meshless or mesh-free methods were developed and they have been extensively studied in mechanical engineering though there are less obvious interests in EM community. The meshless methods employ discrete nodes to replace meshes in the description of geometries but the background meshes for integrations are still needed traditionally. In this work, we first address the traditional meshless scheme for solving EM integral equations based on the moving least square (MLS) approximation for unknown currents and the use of background meshes for integrations, and then develop a novel meshless scheme by applying the Green's lemma to the EM surface integral equations with flat domains. The novel scheme transforms a surface integral over a flat domain into a line integral along its boundaries when excluding a singular patch in the domain. Since only the domain boundaries are discretized and no background meshes are needed, the scheme is truly meshless. Numerical examples for EM scattering by flat-surface objects are presented to demonstrate the effectiveness of the novel scheme. [ABSTRACT FROM PUBLISHER]

We present a new multilevel matrix compression method (MLMCM) and its application to the analysis of scattering problems from three-dimensional (3-D) arbitrary-shaped conductors. The compression is achieved without generating the full subblocks of the matrix by the rank-based method. Unlike the conventional rank-based method, incoming compression matrix \bf U and outgoing compression matrix \bf V are defined when coupling with a cluster of its far interaction groups. Only a small translation matrix \bf D is redefined for every two coupling groups. The merits of the proposed method are: 1) it is kernel function-independent and can be applied to arbitrary complex media; 2) it is more efficient than conventional rank-based methods. This paper shows numerical results to demonstrate the validity of the proposed method. [ABSTRACT FROM PUBLISHER]

Using a variational method, we recently determined an electromagnetic “signature” for characterizing a straight wire in free space. The signature consists of the first five resonant frequencies and their widths, more compactly expressed as the first five complex-valued resonant frequencies. Here we apply the variational method to the much more complicated case of determining the same signature for a straight wire or wire pair on a flat interface between a homogeneous earth and air. To calculate the resonances we obtain an integral equation for the current on a wire on the interface between two dielectric media. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current in an equivalent thin strip on the interface has non-zero solutions. The variational method extracts good approximations to these complex-valued resonant frequencies, without having to solve the integral equation. A table of resonances is given for the case of a relative dielectric constant of the earth equal to 4 and for three values of the ratio of wire radius to wire half-length. [ABSTRACT FROM AUTHOR]

Typical method of moments solution of integral equations for electromagnetics relies on defining basis functions that are tightly coupled to the underlying tessellation. This limits the types of functions (or combinations thereof) that can be used for scattering analysis. In this paper, we introduce a framework that permits seamless inclusion of multiple functions within the approximation space. While the proposed scheme can be used in a mesh-less framework, the work presented herein focuses on implementing these ideas in an existing mesh topology. A number of results are presented that demonstrate approximation properties of this method, comparison of scattering data with other numerical and analytical methods and several advantages of the proposed method; including the low frequency stability of the resulting discrete system, its ability to mix different orders and types of basis functions and finally, its applicability to non-conformal tessellations. [ABSTRACT FROM PUBLISHER]

With an interest in finding wires and distinguishing them from other electrically conducting objects, we have looked for an electromagnetic “fingerprint” in terms of resonances of a straight wire of length 2h and radius a. The resonances of the wire are formulated using the theory of the linear antenna, leading to an integral equation for the current on the wire. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current on the wire has non-zero solutions. By applying a variational technique we obtain approximate numerical solutions for the resonant frequencies and their widths. A table of the first five resonances is given for several ratios of wire half-length h to wire radius a. In a subsequent paper we propose to extend the method described here to deal with wires on an earth-air interface, for example as used to command the detonation of improvised explosive devices. [ABSTRACT FROM AUTHOR]

An efficient technique is proposed to compute the scattering or radiation from/by 1-D periodic structures residing in a layered background medium. The technique is based on a mixed potential integral equation (MPIE) combined with the method of moments (MoM), solving for the unknown current density flowing within a unit cell of the periodic structure. The formalism requires the knowledge of the pertinent layered medium Green's functions with 1-D periodicity. Here, these Green's functions are derived in closed-form by invoking the perfectly matched layer (PML)-paradigm. The stationary phase method is applied to determine the far field of the infinite, periodic structure, leading to a series of Floquet modes. In addition, approximating this series leads to an efficient technique to estimate the scattering or radiation from/by large, but finite, periodic structures with a 1-D periodic character. The theory is illustrated and validated by means of various examples, stemming from scattering and radiation applications from/by antenna arrays residing on microstrip substrates. The efficiency of the method is also demonstrated. [ABSTRACT FROM PUBLISHER]

The (numerical) solution of a rectangular crack in a perfectly conducting surface is appropriate for non-destructive testing (NDT) applications to model faults. The paper presents a direct modeling technique for determining the H and E-polarized backscattering signatures of a two-dimensional crack in a metallic surface that is suitable for inverse scattering problem. The governing field integral equations (FIE) with logarithmic and hyper singular kernels is first discretized and solved by a collocation method based on Chebyshev polynomials. By using ad hoc quadrature rules, the integral equation is then reduced to a linear system of algebraic equations. This approach does not have the size or frequency limitations of the regular techniques such as modal expansion and quasi-static manners. The results are in good agreement with the entirely numerical and non-reversible solution of a finite element method. [ABSTRACT FROM AUTHOR]

A powerful technique for solving electromagnetic (EM) surface integral equations (SIE5) for inhomogenous objects by the method of moments (MoM) involves the well-known Rao-Wilton-Glisson (RWG) basis function to represent the electric current and, for field orthogonality and numerical stability reasons, a variation of the RWG basis known as the ̂n x RWG basis (where ̂n is a unit normal vector at the object surface) to represent the magnetic current. Though this combination provides a numerically efficient and effective solution that has been demonstrated on a variety of structures, one cannot feel entirely comfortable because of the presence of fictitious magnetic current associated with the modified basis. Chen and Wilton proposed a different, smoother basis in 1990 that avoids the fictitious line charges, but because of computational cost issues it has not been used beyond Chen's dissertation. Recently, this basis was rediscovered and has received considerable attention. Our work reexamines the dual basis, exploring issues not addressed by Chen and Wilton and showing accurate solutions for a variety of EM scattering structures. [ABSTRACT FROM AUTHOR]

The time-harmonic electromagnetic scattering from conducting surfaces is considered. In this context, a recently published model order reduction for frequency interpolation of the surface current via singular value decomposition (SVD) is analyzed and evaluated: the exact currents computed at Q frequencies are arranged columnwise in a matrix, the SVD of which provides an orthonormal basis; on account of the observed exponential decrease of the singular values of this matrix, it is assumed that the dimension of the basis required for an accurate interpolation is much smaller than the number of unknowns in the original formulation. We propose in this paper a formal framework that justifies this decrease of the singular values, as well as the corresponding behavior of the interpolation error made on the current. From considerations based on high-frequency electromagnetics, it is shown that this method can be interpreted in terms of sampling criteria for the current, that yield an a priori estimate for the minimum value of Q. Numerical examples illustrate the capacities of this technique for frequency interpolation and for high-frequency analysis of the currents. [ABSTRACT FROM AUTHOR]

The scattering cross section data obtained from numerical solutions of the magnetic field integral equation (MFIE), using a variety of basis functions and both Galerkin and non-Galerkin testing schemes, are compared to study the convergence rates of the results. For the basis functions considered, apparent superconvergence is observed in the MFIE scattering cross section when linear tangential/linear normal vector basis functions are used with Galerkin testing, but not with other basis functions. [ABSTRACT FROM AUTHOR]

The time-harmonic electromagnetic scattering or radiation problem is considered. The singular value decomposition (SVD) is applied to the radiation operator that maps the set of electric and magnetic currents defined on the surface of an inhomogeneous object onto the set of the far-fields scattered (or radiated) from this object. The SVD yields orthonormal bases for both sets. Because the radiation operator is compact and regularizing, it is demonstrated that the far-field calculated from the series expansions of the currents on these bases converges exponentially fast to the exact one if a sufficient number of terms is considered in these series. This number is closely related to the degrees of freedom that characterize the far-field. The latter can be computed from a reduced number of unknowns in the discretized integral equation that links electric and magnetic surface currents by writing it in the new currents bases. Also, it allows the reduction of the far-field in a given angular sector. The numerical complexity of this technique is addressed, and 2D numerical examples are presented that illustrate its potentialities. [ABSTRACT FROM AUTHOR]

In the calculation of the radiation patterns of antennas installed on complex structures using iterative solvers, the convergence rate is often slower compared to the problem with the structure alone without antenna. This is due to the resonant nature of the antenna. To increase the convergence rate, a resonant extraction method is introduced by which a small region including the antenna and its nearby neighborhood is singled out from the overall structure and treated using a direct method, and a reduced system is better conditioned, hence much less iteration numbers are needed if solved by an iterative solver. Numerical examples are provided to demonstrate the effectiveness of this method. [ABSTRACT FROM AUTHOR]

Based on correlation receiver in communication theory, the measured backscattering waveform of a calibration conducting sphere is adopted as the system impulse response. This antenna-target system response is then approximated by the derivatives of a Gaussian function (DGF) as well as the Coiflets to restore the impulse response of the target and to reconstruct the ISAR images. Both the DGF and Coiflets are applied to the deconvolution and their results are compared. The Gaussian and Coiflet function parameters are derived by a best-fit to the measured time-domain system response. Employing the parametric fits, a lowpass filter has been automatically embedded which performs regularization of the conjugate gradient (CG) optimization and speeds up the CG convergence. Numerical results show that the image quality from the Coiflet system is similar to or better than from the DGF system. Owing to the continuity, smoothness, orthogonality and compact support of the Coiflets, the size of the system matrix has been reduced from 1024 × 1024 for DGF to 261 × 261, and the deconvolution process is accelerated more than 22 fold without sacrificing image characters. [ABSTRACT FROM AUTHOR]

A domain decomposition scheme based on the equivalence principle, similar to Huygens' principle, for integral equation solvers and the method of moments is introduced. The equivalence principle allows the replacement of unknown currents distributed in a volume in space by equivalence currents residing on the surface that bounds the volume. It also allows the dissociation of the solution of one region from that of another region. In this manner, problems of high complexity can be encapsulated by surfaces of simpler shapes using less unknowns. It can aid in parallel algorithms, reusability of solutions, as well as improving the condition number of a matrix system when disparate mesh or adaptive mesh are needed. The challenge arises when an equivalence surface intercepts a current-carrying conductor, because the breakup of the current into separate pieces gives rise to charge singularity. A junction basis can be used to mitigate this singularity. However, a better solution is to introduce a tap basis to model the current that intercepts with the equivalence surfaces. Using this scheme, the current continuity is conserved and the singularity of the charges is avoided. The solution is shown to be accurate. [ABSTRACT FROM AUTHOR]

We present physical concepts and formulations for a parallel-plate waveguide which is partially filled with stratified right-handed and left-handed media and fed by apertures. Based on an exact analysis, high power transmissions can be obtained if the medium parameters and layer thicknesses are properly chosen. Such a structure is called a super waveguide since the transmitted power is extremely larger than that in a conventional air-filled waveguide. The equivalence principle and stratified medium theory are used to set up the integral equation in terms of the magnetic currents on apertures. We have applied the method of moments to discretize the integral equation and solved it numerically. The impact of such magnetic currents to the high-power transmission and their interaction to the original dipole source are investigated. From numerical results, we notice that the transmission power is not as high as we anticipated if the source is outside the waveguide. If the source is placed inside the waveguide through apertures, however, the super waveguide will be realized. [ABSTRACT FROM AUTHOR]

A hybrid approach of the generalized forward-backward method (GFBM) with spectral accelerate algorithm (SAA) and Monte Carlo method is developed in this paper. It is applied to numerical simulation of bistatic scattering from one-dimensional arbitrary dielectric constant soil surface with a conducting object partially buried under the horizontal and vertical tapered wave incident at low grazing angle. The energy conservation is used to valuate accuracy of the GFBM/SAA. Numerical simulations of bistatic scattering at low grazing angle are discussed in this paper. [ABSTRACT FROM AUTHOR]

The hybrid volume and surface integral equation approach is applied to solve electromagnetic scattering and radiation problems involving conducting and/or dielectric objects. To flexibly and accurately model the complex structures and reduce the number of unknowns, mixed mesh scheme is developed to discretize the object. In this scheme, the triangles and quadrangles are used to discretize the conducting part of the object, and the tetrahedrons, hexahedrons, prisms and pyramids are used to model the dielectric volumes of the scatterer. Numerical results showed the solution accuracies from the mixed element meshes are of the same level compared with the single element meshes, but uses much less number of unknowns. This leads to flexibility for mesh generating and reduces the we of computing resources. [ABSTRACT FROM AUTHOR]

We consider the time-harmonic electromagnetic scattering problem from a finite planar or curved structure made up of infinitesimally thin frequency-selective surfaces (FSSs) embedded in dielectric layers, with possibly nearby located objects. In order to avoid the meshing of the unit cells that constitute the FSSs, this problem is solved by employing an integral equation (IE) or finite-element (FE) formulation in conjunction with approximate impedance boundary conditions (IBCs) prescribed on the sheets that model the FSSs. The impedances in the IBCs are derived from the exact reflection and transmission coefficients calculated for the fundamental Floquet mode on the infinite planar structure illuminated by a planewave at a given incidence. When the structure is curved and/or the direction of the incident wave is unknown, higher order IBCs are proposed that are valid in a large angular range and can be implemented in a standard IE or FE formulation. Their numerical efficiencies are evaluated for finite planar or curved two-dimensional structures, or radomes, where the FSSs are strip gratings. As an example, for a curved radome surrounding a conducting plate, it is shown that, when the Floquet modes of the gratings are evanescent, these IBCs allow an accurate calculation of the radar cross section of the whole structure with far smaller computing resources than would have been required by a full-wave formulation. [ABSTRACT FROM AUTHOR]

Electromagnetic penetration through an aperture into a cavity is considered. The structure of interest is a semielliptical channel flush-mounted under a metal plane and slotted along the interfocal distance of its cross-section. The channel is filled with a material isorefractive to the medium that occupies the half-space above the metal plane. Three independent integral equations are developed to compute the currents induced on the structure of interest by plane wave and line source excitations. Numerical results from the integral equation methods are compared with the evaluation of the analytical expressions, derived in a previous paper, that involve the summation of Mathieu functions. Data are presented for two polarizations, various values of intrinsic impedances and ratio between aperture width and incident radiation wavelength. Further data are presented for the bistatic radar cross-section of the structure of interest. All data obtained from the integral equation methods and the evaluations of the analytical formulas are in excellent agreement. [ABSTRACT FROM AUTHOR]

The residual error incurred when numerically solving integral equations for a number of electromagnetic radiation and scattering problems is calculated with the aid of an overdetermined system. This error is systematically reduced by adaptively refining the model for the surface current. Error reduction is achieved by selectively shrinking cell dimensions (h-refinement), increasing the order of the basis functions representing the current (p-refinement), or a combination of both (hp-refinement). The correlation between residual error and surface current error is investigated and found to be high. The impact of edge singularities and curvature discontinuities is discussed. [ABSTRACT FROM AUTHOR]

A technique based on the surface integral equation is applied for the analysis of antenna radiation in the presence of an arbitrarily shaped dielectric radome terminated by a conducting surface. The equivalence prineciple is used to characterize the effect of the radome on the transmitted field in terms of equivalent surface electric and magnetic currents which radiate in an unbounded medium. A set of coupled integral equations involving these currents is obtained by using the boundary conditions on the tangential components of the total fields. The adaptive integral method is applied to solve the integral equations so that electrically large radomes can be analyzed. The radiation patterns of dipole arrays with dielectric radomes of super spheroidal shape are also presented. [ABSTRACT FROM AUTHOR]

A method of fast computation of the mixed potential Green's functions (MPGFs) in spatial domain for cylindrically stratified media has been developed. Based on the convergence behavior of the MPGFs in spectral domain, the discrete complex image method (DCIM) and the extrapolation technique are employed to perform the inverse Fourier transform, which is different from that of planarly stratified media. In order to evaluate the summation of cylindrical eigenmode from order of negative infinity to order of positive infinity, the Green's functions in spectral domain are rearranged so that acceleration technique can be well applied to speed up the convergence of summation process. For the integral along the deformed Sommerfeld integral path with respect to kz, DCIM is used to speed up the computation. After the quasistatic components are completely subtracted from the spectral domain Green's functions, the inverse transform of the remaining parts has an approximated analytical form. The proposed method can be used to accurately and efficiently calculate the spatial domain MPGFs, which are useful for characterizing conformal patch structures mounted on cylindrically stratified media. [ABSTRACT FROM AUTHOR]

This paper presents an efficient technique for evaluating Green's functions associated to layered media, when formulated as Sommerfeld integrals in the space domain. The key step in the formulation is that Sommerfeld integrals are computed choosing a suitable integration path which is closed through the imaginary axis of the complex spectral plane. It is shown that with this original choke of the integration contour, the numerical effort usually involved in the evaluation of Sommerfeld integrals can be greatly reduced, specially when large source-observer distances are involved. One asset of this technique is that it can be easily incorporated into integral equation based CAD packages for the efficient analysis of complex printed microwave circuit and antennas. In addition, the theoretical developments needed to set up the numerical algorithm throw a new light on the asymptotic behavior of the layered media Green's functions for large source-observer distances. [ABSTRACT FROM AUTHOR]

The locally corrected Nyström method is used to solve the electric field integral equation to determine the currents and input impedance of a hollow linear dipole. The results suggest that the Nyström method, despite the use of a discontinuous underlying representation for the currents, can produce currents and input impedance comparable in accuracy to those obtained by the method of moments. [ABSTRACT FROM AUTHOR]