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In this paper, we formulate a recently proposed qualitative imaging approach named near-field orthogonality sampling method (NOSM) for a general measurement configuration. In the very first version, the NOSM was basically a backpropagation method, which analytically transforms the scattered fields, which is obtained with some specific multiview–multistatic measurement configurations (circular or linear), to reduced scattered electric fields on the sampling domain, which encapsulates the targets. The contributions of this paper are: 1) physical meaning of the reduced scattered field of the NOSM is explained by showing how it approximates the contrast source values in the sampling domain for different generic and limited aperture configurations; 2) the application of the NOSM is generalized to a generic configuration and some comments are made how to reduce the computational complexity and source requirements; 3) the reciprocity of the data is accounted for to improve the performance for limited aperture measurement scenarios; and 4) finally, a useful modified indicator is obtained by relying on the physical meaning of the indicator. The accuracy and stability of the proposed formulations are corroborated with numerical examples for which the excitation-measurement configuration is of limited aperture. [ABSTRACT FROM AUTHOR]

Singular divergence-conforming bases have been proposed for the solution of integral equations although they have seen only occasional use in practical applications. The existing singular bases are not hierarchical, which prevents their use in adaptive $ {p}$ -refinement applications. In this paper, a new family of singular hierarchical basis functions is proposed for quadrilateral cells. These functions model the singularities associated with current and charge density at edges and are more convenient for modeling such singularities than triangular bases of the same kind. The basis functions are of the additive kind and combine a hierarchical polynomial representation on quadrilaterals with linearly independent singular terms that incorporate general exponents that may be adjusted for the specific wedge angle of interest. Moreover, the added singular basis functions are computed on the fly. On the basis of various reported numerical results, this paper also illustrates the difficulties, the advantages, the accuracy, and the cost of using such bases in the method of moment solutions of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we present a new methodology for a nonoverlapping domain decomposition method using boundary integral equations and adaptive cross approximation in the frequency domain (IE-ACA-DDM). This paper proposes two main novelties. First, the IE-DDM condition number is improved with the development of a formulation based on electric field integral equation (EFIE) implementation over the entire subdomains and on a simplification of the magnetic field integral equation (MFIE) on the interfaces. As a consequence, the number of matrix–vector products is significantly reduced during the iterative resolution. Then, this paper proves that the ACA can be applied and efficiently implemented in IE-DDM methods. Moreover, a hierarchical LU (HLU) decomposition is proposed to accelerate the ACA solver. The IE-ACA-DDM is very suitable for the resolution of multiple excitations and to bypass the low-frequency breakdown. The flexibility, accuracy, and efficiency of IE-ACA-DDM are demonstrated by comparing with reference integral equation solutions and scaled mock-up measurements. [ABSTRACT FROM PUBLISHER]

The electric field integral equation is a well-known workhorse for obtaining fields scattered by a perfect electric conducting object. As a result, the nuances and challenges of solving this equation have been examined for a while. Two recent papers motivate the effort presented in this paper. Unlike traditional work that uses equivalent currents defined on surfaces, recent research proposes a technique that results in well-conditioned systems by employing generalized Debye sources (GDS) as unknowns. In a complementary effort, some of us developed a method that exploits the same representation for both the geometry (subdivision surface representations) and functions defined on the geometry, also known as isogeometric analysis (IGA). The challenge in generalizing GDS method to a discretized geometry is the complexity of the intermediate operators. However, thanks to our earlier work on subdivision surfaces, the additional smoothness of geometric representation permits discretizing these intermediate operations. In this paper, we employ both ideas to present a well-conditioned GDS-electric field integral equation. Here, the intermediate surface Laplacian is well discretized by using subdivision basis. Likewise, using subdivision basis to represent the sources results in an efficient and accurate IGA framework. Numerous results are presented to demonstrate the efficacy of the approach. [ABSTRACT FROM PUBLISHER]

Complex scattering targets are often made by structures constituted by wedges and penetrable substrates which may interact at near field. In this paper, we describe a complete procedure to study this problem with possible developments in radar technologies (like GPR), antenna development, or electromagnetic compatibility (tips near substrates). The diffraction of an incident plane wave by a perfectly conducting (PEC) wedge over a dielectric half-space is studied using generalized Wiener–Hopf equations (GWHEs), and the solution is obtained using analytical and numerical–analytical approaches that reduce the Wiener-Hopf (WH) factorization to integral equations (IEs). The mathematical aspects are described in a unified and consistent theory for angular and layered region problems. The proposed procedure is valid for the general case and the paper focuses on E-polarization at normal incidence. The solutions are given in terms of geometrical/uniform theory of diffraction (GTD/UTD) diffraction coefficients and total far fields for engineering applications. This paper presents several numerical test cases that show the validity of the proposed method. [ABSTRACT FROM AUTHOR]

For the case of perfectly conducting (PC) antennas, the difficulties inherent in the process of discretizing, certain thin-wire integral equations were examined in detail in the literature by means of an analytical study of the antenna of infinite length. This paper extends the previous results to corresponding integral equations applicable to carbon nanotube antennas. Connections between the finite and infinite cases are discussed in detail. While there are many similarities with the PC case, we show that there exist new difficulties, with no counterpart for the PC antennas. We discuss their nature through both the analytical and numerical results. [ABSTRACT FROM AUTHOR]

In this paper, the physical meanings and various computing methods of characteristic modes (CMs) of dielectric and magnetic bodies are investigated. Two types of surface integral equation (SIE) formulations based on the dependent relationships between the equivalent surface electric and magnetic currents are proposed. Following the two types of SIE formulations, two generalized eigenvalue equations are established to determine the CMs of dielectric or magnetic bodies. This is in contrast to the approach using induced volume currents. It is found that the eigenvalues possess clear physical meanings similar to those of perfectly electric conducting bodies. The CMs can be used to describe the resonant features, including resonant frequencies and resonant field distributions. Numerical results are presented to validate the proposed formulations. [ABSTRACT FROM AUTHOR]

This paper presents a finite-element method (FEM), based on a new set of vector basis functions, for an efficient solution of the electromagnetic scattering problem from a continuously varying inhomogeneous sphere. The new bases lead to a large number of similar terms in the entries of the finite-element matrix and make the interaction between the inner and outer field expansions’ diagonal. The method is compared with a tetrahedral-based FEM, and the efficiency of the method is investigated through some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) method is used to solve the electromagnetic scattering problem for 3-D inhomogeneous uniaxial anisotropic objects embedded in a layered uniaxial medium. The optical axis of the background medium is perpendicular to the layer boundaries. However, the optical axis of the scatterer can be rotated through any angles. The electric field integral equation (EFIE) is formulated in the layered uniaxial anisotropic background medium. The volumetric roof-top function is used for the basis function as well as the testing function. The dyadic Green’s functions (DGFs) for both the electric field and the magnetic vector potential are used to solve the EFIE, and the results as well as the performance are compared. Several numerical simulations are carried out to validate the accuracy and efficiency of the proposed method. The major new contribution of this paper is to extend the BCGS-FFT method to accommodate the uniaxial anisotropy of the layered background medium. Therefore, the DGFs for the layered uniaxial medium are evaluated before solving the EFIE. In addition, the DGF for the electric field is also used to solve the 3-D scattering problem through BCGS-FFT iterations, which is different from the previous work. [ABSTRACT FROM AUTHOR]

The use of the method of moments to solve surface integral equations is one of the most popular numerical techniques in electromagnetic modeling and analysis. This method requires the accurate and efficient numerical evaluation of iterated surface integrals over both source and testing domains. In this paper, we propose a scheme for evaluating these 4-D interaction integrals between pairs of arbitrarily positioned and oriented elements. The approach is based on applying the surface divergence theorem twice, once on the source and once on the test domain. When the integrations are reordered as two outer contour integrals plus two inner radial integrals, the initial radial integrations provide significant smoothing of the underlying singular integrands. The method is numerically validated for static and dynamic kernels arising in the electric field integral equation, i.e., for kernels with $1/R$ singularities, and linear basis functions. The proposed formula to evaluate 4-D reaction integrals can be extended to different kernels and to different elements, e.g., to curved or volumetric elements, and to basis functions of higher order. [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]

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]

The optimal locations of transmitters in a building, that best meet the bandwidth requirements of all users, was studied in the past by a small number of authors. They used empirical path loss models to constrain an optimization cost function. This paper concentrates on using a signal-to-interference ratio cost function with realistic field parameters obtained using a fast ray-tracing algorithm. The solution obtained is shown to perform well in realistic scenarios, meeting a large proportion of user bandwidth requirements. However, it does not perform well in an oversaturated environment. [ABSTRACT FROM PUBLISHER]

This paper reports experiments on single and dual electromagnetic jets (also called photonic jets) emerging from a weakly multimode waveguide excited by a plane wave in the microwaves frequencies (30 GHz), ended with a tip with a special shape. The measurements are performed with a two-dimensional spatial field mapping system. This system acquires the electric field distribution at the end of the tipped waveguide. Qualitatively, the electric field maps confirm the presence of photonic jets that were recently predicted by a computational model based on boundary integral equations. Backscattering induced by the interaction of a particle with the electromagnetic jet is also measured; particles with a size smaller than the incident wavelength can be easily detected. The high sensitivity feature of the backscattering can be used to develop a near-field technique for microwave or optical imaging. [ABSTRACT FROM PUBLISHER]

Scattering targets are often made by complex structures constituted by thin metallic plates as wings, fins, winglets. When thin plates are connected together, they define surface junctions with the possible presence of sharp edges. In this paper we describe a complete procedure to handle junctions in presence of sharp edges in surface integral equation methods by defining the required basis functions and unknowns. This approach is based on the use of divergence-conforming higher order interpolatory vector basis functions, singular vector basis functions and on Kirchhoff's current law. The paper presents several numerical test cases that show the instability of solutions using classical methods and the full convergence of the proposed numerical scheme. [ABSTRACT FROM PUBLISHER]

A new approach to the implementation of the Fredholm integral method (FIM) was developed to evaluate scattering by irregular dielectric particles. In this paper, particles are modeled discretizing their volume with cells according to their weighted contents. The approach to FIM presented in this paper represents a departure from earlier work where the numerical integration is no longer based on expansion in a set of polynomials but on direct spatial integration. This approach which still involves contour integration method uses quandrantal contour in combination with a conditioning weighting function to control the magnitude of the integrand due to the power of the radial variable in the integrand being odd. The strength of our approach lies on the fact that computations are performed in the spatial frequency domain. As a result, the angular scattering pattern is strongly connected to the spatial Fourier transform of the scatterer; hence, for electrically small particles the angular spectrum is relatively smooth and the number of pivots required for integration is relatively low. This technique is well suited to the treatment of scattering from irregular inhomogeneous dielectric particles since only the distribution in space of the dielectric constants needs to be defined. Numerical results also confirm the inadequacy of effective medium theories in evaluating scattering characteristics of inhomogeneous particles. [ABSTRACT FROM AUTHOR]

This contribution presents a novel Windowed Green Function (WGF) method for the solution of problems of wave propagation, scattering, and radiation for structures that include open (dielectric) waveguides, waveguide junctions, as well as launching and/or termination sites and other nonuniformities. Based on the use of a “slow-rise” smooth-windowing technique in conjunction with free-space Green functions and associated integral representations, the proposed approach produces numerical solutions with errors that decrease faster than any negative power of the window size. The proposed methodology bypasses some of the most significant challenges associated with waveguide simulation. In particular, the WGF approach handles spatially infinite dielectric waveguide structures without recourse to absorbing boundary conditions, it facilitates proper treatment of complex geometries, and it seamlessly incorporates the open-waveguide character and associated radiation conditions inherent in the problem under consideration. The overall WGF approach is demonstrated in this paper by means of a variety of numerical results for 2-D open-waveguide termination, launching and junction problems. [ABSTRACT FROM AUTHOR]

In this paper, a simple solution is presented for multifrequency electromagnetic scattering from inhomogeneous bodies. Shifted frequency internal equivalence is used to replace the electromagnetic problem at operating frequency $\omega $ by equivalent volume and current sources at internal frequency \omega _{0} , and hence repeated calculation of system matrix as in the solution of volume integral equation at multiple frequencies is avoided. The volume field equation and surface tangent field equations obtained from the internal and external problems, the substitutes of the original scattering problem internally and externally, are solved by method of moments with pulse function expansion and point matching. Numerical results demonstrate that the proposed method is accurate and efficient within a wideband, fractional bandwidth being typically 100%. [ABSTRACT FROM AUTHOR]

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]

A discontinuous Galerkin (DG) augmented electric field integral equation method based on the domain decomposition is proposed in this paper for full-wave solution of multiscale targets. The conventional surface integral equation-based DG method allowing both conformal and nonconformal discretizations for multiscale structures suffers from low-frequency breakdown. By augmenting the DG-EFIE with current continuity equation, the proposed scheme can alleviate the low-frequency breakdown. In the augmented system, the electric field integral equation and the current continuity equation are discretized by using hybrid basis functions including Rao–Wilton–Glisson (RWG) and half RWG basis functions. Since the half RWG basis is not divergence conforming, line charge degrees of freedom on the adjoining edges are introduced in this paper. It is observed that the resulting linear system is well conditioned at low frequencies, which leads to a rapid convergence over wide frequency band. Numerical examples demonstrate the accuracy and efficiency of the augmented system. [ABSTRACT FROM AUTHOR]

In this paper, we improved the performance of the contrast source inversion (CSI) method by incorporating a so-called cross-correlated cost functional, which interrelates the state error and the data error in the measurement domain. The proposed method is referred to as the cross-correlated CSI. It enables better robustness and higher inversion accuracy than both the classical CSI and multiplicative regularized CSI (MR-CSI). In addition, we show how the gradient of the modified cost functional can be calculated without significantly increasing the computational burden. The advantages of the proposed algorithms are demonstrated using a 2-D benchmark problem excited by a transverse magnetic wave as well as a transverse electric wave, respectively, in comparison with classical CSI and MR-CSI. [ABSTRACT FROM PUBLISHER]

A new and general partial element equivalent circuit (PEEC) formulation based on electric and magnetic vector potentials and the cell method is presented. The purpose of this paper is manifold. First, a comprehensive review of well-established PEEC method is given and the state-of-the-art of the method with focus on the inclusion of magnetic media in the formulation is discussed. Then, a new and general formulation of the PEEC method based on integral equations is proposed. The formulation is valid for conductive, dielectric, and magnetic media and its advantages with respect to the state-of-the-art PEEC formulations are underlined. Unlike the existing PEEC methods, this novel formulation, thanks to the reinterpretation of PEEC in the context of integral equation methods, allows for maintaining a circuit interpretation for both electric and magnetic media. Thus, a standard Spice-like solver can in principle be adopted for the solution of electromagnetic (EM) problems also when magnetic media are involved. The imposition of the divergence condition for the current density vectors is guaranteed and also the case of inhomogeneous and anisotropic media is considered. A thorough discussion on the suitability of the method for the study of both low- and high-frequency EM problems is also presented. Finally, the case study of a near-field communication antenna is considered as an example of the applicability of the formulation to problems of industrial interest. Comparisons with commercial softwares, measurements, and the state-of-the-art PEEC method are given in order to demonstrate the accuracy and the advantages of the proposed PEEC formulation. [ABSTRACT FROM AUTHOR]

In this paper, we present a flexible and efficient ternary parallelization approach for the multilevel fast multipole algorithm (MLFMA) for the solution of extremely large 3-D scattering problems with over 10 billion unknowns. In the ternary parallelization approach, a binary clustering tree of all the message passing interface (MPI) processes is built first. Then, the MLFMA tree is categorized into plane wave partitioning, hierarchical-structure partitioning, and box partitioning (BP) levels via a top–down approach to match the process clustering tree. Compared with the bottom–up approach, interprocess communications in the far interaction are reduced. An inner-group transition level is designed for switching partitions on the intermediate level between the hierarchical-structure partitioning and BP levels. The ternary strategy can realize as high parallel efficiency as the hierarchical partitioning strategy while maintaining flexibility in selecting the total number of processes. An auxiliary-tree-based parallel mesh refinement technique and a hybrid octree storage strategy are designed to facilitate the realization of fast full-wave simulation on a scale of over 10 billion unknowns with the ternary MLFMA. The accuracy of the solutions is validated by comparing the radar cross sections (RCSs) of a sphere of diameter 3042 wavelengths with 10 773 415 728 unknowns via the MLFMA and the Mie series, which is the largest number of unknowns to be computed via full wave numerical methods to date. Furthermore, the solutions for complicated objects, namely a ship and an aircraft model, both of which have maximum lengths that exceed 10 000 wavelengths and over 10 billion unknowns, are presented. [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]

Electromagnetic scattering from electrically large objects with multiscale features is an increasingly important problem in computational electromagnetics. A conventional approach is to use an integral equation-based solver that is then augmented with an accelerator, a popular choice being a parallel multilevel fast multipole algorithm (MLFMA). One consequence of multiscale features is locally dense discretization, which leads to low-frequency breakdown and requires nonuniform trees. To the authors’ knowledge, the literature on parallel MLFMA for such multiscale distributions capable of arbitrary accuracy is sparse; this paper aims to fill this niche. We prescribe an algorithm that overcomes this bottleneck. We demonstrate the accuracy (with respect to analytical data) and performance of the algorithm for both PEC scatterers and point clouds as large as $755{\lambda }$ with several hundred million unknowns and nonuniform trees as deep as 16 levels. [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]

The analysis for large-scale antenna arrays is a hot topic for design and optimization. In this paper, an efficient method for analyzing antenna arrays by using characteristic mode (CM) is proposed. In order to analyze common antennas composing of conductor and dielectric, the theory of CM is first introduced into the volume-surface integral equation. An auxiliary general eigen-equation is established to make the modes orthogonal. Furthermore, a source mode (SM) is constructed to modify the accuracy when using CMs to expand the currents excited by a delta gap source for antenna problems. To demonstrate the influence of antenna structures and excitations on the CM and SM, three antennas are analyzed and only a few modes are required to achieve a good accuracy. Due to the periodicity of antenna arrays, CMs can be served as entire-domain basis functions defined on one antenna element and reused to reduce the unknowns in the method of moments (MoM). Numerical results have shown that the proposed method can have a good agreement with the traditional MoM. Meanwhile, both the memory requirements and computational time of the proposed method can be significantly reduced. [ABSTRACT FROM AUTHOR]

The focus of this paper is on the volume integral representations to be used in constructing integral equations for composite volume media. The major thrust of the paper is to identify where derivatives of a discontinuous function arise in the derivation of the volume representation. Three different derivation methods are presented, resulting in identical representation independent of the derivation method. These representations agree with some in the existing literature and disagree with others. When an electric field formulation is considered, the source of disagreement manifests itself only when magnetic materials are present. Likewise, for the dual situation, the inconsistency appears for a magnetic field formulation of dielectric materials. This paper identifies the sources of error in the incorrect representations and its major contribution is the rigorously correct derivation of the representations to be used in volume integral equations. We also present numerical results for an integral equation derived from our representation. The numerical results employ only the E-field as the unknown and the singularity is handled in a manner analogous to a standard numerical treatment of the electric field integral equation. [ABSTRACT FROM AUTHOR]

The method of moments solution on integral equations for electromagnetic scattering and radiation problems with Rao-Wilton-Glisson (RWG) and n × RWG basis functions requires the calculation of singular double surface integrals over triangular subdomains. In this paper, an approach is presented to deal with the singularity and almost singularity in which the triangle subdomain is divided into several subtriangles and then the singular or almost singular integral is calculated over each of the subtriangles. This approach is mainly based on the projection process and the local polar frame. It can be used to deal with the singular double surface integrals of order 1/R and 1/R², in which vector functions may be of zeroth-order and higher order. Numerical examples are provided to verify the validity of the method presented in this paper for dealing with the singularity and almost singularity. [ABSTRACT FROM AUTHOR]

This paper presents a single-level matrix compression algorithm, termed IE-QR, based on a low-rank approximation to speed up the electric field integral equation (EFIE) formulation. It is shown, with the number of groups chosen to be proportional to N1/2, where N is the number of unknowns, the memory and CPU time for the resulting algorithm are both O(N1.5). The unique features of the algorithm are: a The IE-QR algorithm is based on the near-rank-deficiency property for well-separated groups. This near-rank-deficiency assumption holds true for many integral equation methods such as Laplacian, radiation, and scattering problems in electromagnetics (EM). The same algorithm can be adapted to other applications outside EM with few or no modifications; and, b. The rank estimation is achieved by a dual-rank process, which ranks the transmitting and receiving groups, respectively. Thus, the IE-QR algorithm can achieve matrix compression without assembling the entire system matrix. Also, a "geometric-neighboring" preconditioner is presented in this paper. This "geometric-neighboring" preconditioner when used in conjunction with GMRES is proven to be both efficient and effective for solving the compressed matrix equations. [ABSTRACT FROM AUTHOR]

For a 2-D problem and at microwave radar frequencies, in a previous paper, the field scattered by a highly conducting large rough sea surface in the presence of a duct having a linear-square refractive index profile has been computed. The forward–backward (FB) method has been applied to solve the linear system obtained by discretizing the boundary integral equation from the method of moments. To reduce again the complexity in order to solve huge problems, the subdomain decomposition iterative method is applied and combined with the FB spectral-acceleration for the calculation of the surface currents on each subsurface of the sea. The adaptive cross approximation algorithm is also applied to accelerate the coupling steps between the subsurfaces. Finally, this method is tested on the medium having a refractive index of parabolic profile, which is more realistic than a linear profile. [ABSTRACT FROM PUBLISHER]

Five types of surface integral equation (IE) formulations are presented to determine the characteristic modes of dielectric and magnetic bodies. It should be noted that these five formulations are derived in a unified manner. Instead of directly using the IE coefficient matrices of scattering problems, this paper presents the formulations in a more natural and rigorous way. The IE formulations result in the generalized real symmetric eigenvalue equations for the characteristic modes. It is found that the eigenvalues of the first four formulations indicate the negative or positive imaginary part of the complex power of the characteristic modes, which are zero at resonance. The first two IE formulations result in two new generalized eigenvalue equations, while the last three IE formulations lead to the same generalized eigenvalue equations as in the references. Moreover, the first two formulations can be immune from spurious modes from which the third and fourth formulations suffer. [ABSTRACT FROM PUBLISHER]

Accurate and efficient prediction of electromagnetic scattering from inhomogeneous objects in layered medium is one of the most challenging issues in engineering applications. This paper presents the first 3-D higher order hybrid finite-element method (FEM) and method of moments (MoM) for the accurate modeling of inhomogeneous dielectric objects in multilayered medium. The main challenges of this paper include: 1) the integration of these algorithms for layered medium and 2) the higher order computational approach involved in layered medium for high efficiency. In the proposed method, the MoM with the layered medium dyadic Green’s function is used as the exact radiation boundary condition in an inhomogeneous background, and the FEM is applied to model the inhomogeneous objects. Furthermore, the higher order maximally orthogonal basis functions with curl-conforming and divergence-conforming properties are used in the FEM and MoM, respectively to improve the modeling capability of this algorithm. For 3-D inhomogeneous objects scattering in multilayered medium, this new method requires a much more tightly truncated simulation domain than the traditional FEM, and provides much higher flexibility than the pure surface integral equation method. Finally, some numerical results are provided to validate the accuracy, efficiency, and flexibility of this method. [ABSTRACT FROM AUTHOR]

The Galerkin boundary element method (BEM), also known as the method of moments, is a powerful method for solving the Laplace equation in three dimensions. There are advantages to Galerkin formulations for integral equations, as they treat problems associated with kernel singularity, and lead to symmetric and better conditioned matrices. However, the Galerkin method requires the computation of double surface integral over pairs of triangles. There are many semianalytical methods to treat these integrals, which all have some issues and are discussed in this paper. Novel methods inspired by the treatment of these kernels in the fast multipole method are presented for computing all the integrals that arise in the Galerkin formulation to any accuracy. Integrals involving completely geometrically separated triangles are nonsingular, and are computed using a technique based on spherical harmonics and multipole expansions and translations, which require the integration of polynomial functions over the triangles. Integrals involving cases where the triangles have common vertices, edges, or are coincident are treated via scaling and symmetry arguments, combined with automatic recursive geometric decomposition of the integrals. The methods are validated, and example results are presented. [ABSTRACT FROM PUBLISHER]

This paper presents a novel type of basis functions, whose spectral- and space-domain properties can be exploited for the efficient method of moments (MoM) analysis of planar metasurface (MTS) antennas. The effect of the homogenized MTS is introduced in the integral equation as an impedance boundary condition (IBC). The proposed basis functions are shaped as Gaussian-type rings with small width and linear azimuthal phase. The analytical form of the spectrum of the Gaussian ring basis allows for a closed-form evaluation of the MoM impedance matrix’s entries. Moreover, these basis functions account for the global evolution of the surface current density in an effective manner, reducing the size of the MoM system of equations with respect to the case of subdomain basis functions. These features allow one to carry out a direct solution for problems with a diameter of up to 15 wavelengths in less than 1 min using a conventional laptop. The applicability on practical antennas has been tested through the full-wave analysis of MTS antennas implemented with small printed elements. [ABSTRACT FROM PUBLISHER]

For a two-dimensional problem and at microwave radar frequencies, this paper presents a method to compute the field scattered by a highly conducting (the impedance boundary condition is applied) rough sea surface in the presence of a duct having a linear-square refractive index profile below a medium of constant refractive index. In a previous paper, the corresponding Green's function, which allows us to solve the propagation problem, has been derived without considering the sea surface. Using the boundary integral equation (BIE) method, this paper solves jointly the scattering problem from the sea surface and the propagation problem by including this Green's function in the BIE. In addition, to efficiently solve the linear system obtained from the method of moments by discretizing the integral equations, the forward-backward method is applied, which allows us to consider very long rough surfaces. [ABSTRACT FROM PUBLISHER]

Complex scattering targets are often made by structures constituted of wedges that may interact at near field. In this paper, we examine the scattering of a plane electromagnetic wave by two separated arbitrarily oriented perfectly electrically conducting wedges with parallel axes. The procedure to obtain the solution is based on the recently developed semianalytical method known as generalized Wiener–Hopf technique that allows a comprehensive mathematical model of the problem in the spectral domain avoiding multiple steps of interaction among separated objects. The numerical results are presented to validate the procedure in terms of spectral quantities, GTD/uniform theory of diffraction coefficients and total far fields for engineering applications. The structure is of interest in electromagnetic applications, in particular, to accurately predict path loss in propagation with diffraction phenomena. [ABSTRACT FROM AUTHOR]

This paper studies the problem of diffraction of electromagnetic waves on an object containing an arbitrary number of layers of materials with different permittivity and permeability. It is assumed that the typical size of the object is much smaller than the wavelength of the incident wave. In other words, we adopt long-wave approximation and the ratio of these values $k$ is considered a small parameter. In this case, the electromagnetic field can be described by an integral equation using the Stratton–Chu formula. The solution of this equation is sought in the form of a multipole expansion at large distances from the object and in the form of an expansion in the small parameter $k$ in the vicinity of the object. The coefficients in these expansions are determined by solving a recurrence system of electrostatic problems. To illustrate the approach, we consider diffraction of the electromagnetic wave on a cylinder whose cross section consists of two eccentric circles. The proposed scheme for solving diffraction problems is quite simple and does not impose any restrictions on the dielectric and magnetic permeability of the layers. It can be used in the calculation of the scattered electromagnetic field on metal structures as well as on nanoobjects containing layers of metamaterials. [ABSTRACT FROM AUTHOR]

We propose a broadband multilevel fast multipole algorithm using hybridization of the plane wave and the multipole expansions of Green’s function in the analysis of 3-D electromagnetic problems. In the proposed method, the diagonal plane-wave expansion is used for low order harmonics, which captures most of the propagating spectrums, while the dense multipole expansion is used for high order harmonics, which captures most of the evanescent spectrums. By analyzing the errors and choosing the numbers of harmonics accordingly in the plane wave and the multipole expansions, the method is free of low-frequency breakdown and remains accurate at arbitrarily low frequencies, which is similar to the dense fast multipole algorithm (FMA). Meanwhile, the method reduces to the conventional diagonal FMA as the frequency increases. Therefore, it can be regarded as the generalization of the conventional dense and diagonal FMAs. Numerical studies in this paper show that very high accuracies can be achieved using the method. [ABSTRACT FROM AUTHOR]

The standard integral-based microwave tomography suffers from computational limitations associated with Green’s function. Those limitations prevent the image reconstruction process from being fast, which is an important requirement for urgent medical applications such as stroke detection. To cope with these limitations, significant approximations are usually implemented within the integral equations. Those approximations include considering the imaging antennas as point sources, assuming homogeneity along one of the domain’s coordinate axes, and necessitating a background matching medium. These approximations result in some undesirable effects in practice such as reconstructing merely 2-D images with limited accuracy, and manufacturing problems associated with selecting a suitable background matching medium with reasonable dielectric properties. To alleviate some of the above limitations and challenges, this paper introduces a partial differential equation framework for microwave tomography established on the wave and the third Maxwell equations. The proposed method is independent of Green’s function and its corresponding limitations. Thus, it can reconstruct 3-D images in a faster manner, particularly in emergency scenarios such as stroke detection where time is life. To validate the proposed method, realistic biomedical head imaging problems are successfully solved, analyzed, and compared to the standard integral-based microwave tomography in terms of computational time and accuracy. [ABSTRACT FROM AUTHOR]

Modeling the interaction between light and a plasmonic nanoantenna, whose critical dimension is of a few nanometers, is complex owing to the “hydrodynamic” motion of free electrons in a metal. Such a hydrodynamic effect inevitably leads to a nonlocal material response, which enables the propagation of longitudinal electromagnetic waves in the material. In this paper, within the framework of a boundary integral equation and a method of moments algorithm, a computational scheme is developed for predicting the interaction of light with 3-D nonlocal hydrodynamic metallic nanoparticles of arbitrary shape. The numerical implementation is first demonstrated for the test example of a canonical spherical structure. The calculated results are shown to be in the excellent agreement with the theoretical results obtained with the generalized Mie theory. In addition, the capability of treating 3-D structures of general shapes is demonstrated by ellipsoids and dimers. [ABSTRACT FROM AUTHOR]

In this paper, closed-form (Cf.) expressions for the backscattered radar cross section of cylindrically curved perfect electrically conducting plates have been derived. These Cf. expressions have been validated using full-wave integral equation-based solver for several radii (angles) of curvature of the curved plates. Here, the plane wave is incident symmetric with respect to the edges of the curved plate for both convex and concave side incidence cases. Cf. expressions include the contributions due to the reflected rays and the single edge diffracted rays for the convex side incidence case. In addition, the double edge diffracted rays have also been considered for the concave side incidence. The Cf. expressions have been demonstrated to be valid for all angles of curvature for the case of convex side incidence, whereas for the concave side incidence case, they are applicable up to 90° curvature, beyond which the higher order and surface diffracted rays become significant due to the concave nature of the curved plate. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient method to analyze scattering from an inhomogeneous body of revolution (BOR) with anisotropic electromagnetic properties. Both the permittivity and the permeability are assumed to be generalized tensors while there are no restrictions on the geometry of the BOR. The proposed method involves three stages. First, the volume equivalence principle is used to replace the BOR with volume electric and magnetic current densities. Requisite volume integral equations (VIEs) are, then, derived with the electric and magnetic flux densities inside the BOR being the unknown quantities. Finally, the VIEs are solved by Galerkin’s method of moments. This is done by expanding the unknown flux densities in terms of appropriate basis functions compatible with the problem symmetry, and hence, reducing the integral equations to a matrix equation. The formation of the resultant matrix equation is elucidated in detail, whereby it is shown that the computation burden is remarkably reduced as no double volumetric-type integrals are to be computed. The efficiency of the proposed method is demonstrated by comparing the simulation results of several case studies with those available in the literature, or computed by commercial numerical codes. [ABSTRACT FROM AUTHOR]

Previous studies have demonstrated that the representation of the electromagnetic field scattered by a homogeneous object at a given frequency in terms of modes independent of its permittivity can be useful to investigate resonant scattering phenomena, and to design metamaterials. However, these modes have never been calculated for arbitrarily shaped particles in the full-retarded regime. In this paper, we introduce a numerical method based on volume integral equations (VIEs) for their calculation. We show, by studying the electromagnetic scattering from a finite-length cylinder of dimensions comparable to the incident wavelength, that only a moderate number of modes are needed to accurately describe the scattered far-field. Moreover, the presented modal expansion is computationally advantageous compared to the direct solution of the VIE when the scattered field has to be computed for many different values of the dielectric permittivity, given the size, and shape of the dielectric body. [ABSTRACT FROM PUBLISHER]

The compressive sensing (CS) is a new sampling paradigm that promises to accurately reconstruct compressible signals from much fewer measurements than nominal number of data points. To apply the attractive properties illustrated above, a new method named CS-FEKO is proposed in this paper, which introduces the ideas from CS into commercial software field computations involving bodies of arbitrary shape (FEKO) to improve the efficiency of FEKO in solving multistatic scattering problems. In performing a multistatic scattering analysis with CS-FEKO, the far-zone scattered fields in one scattering angle over all excitations are viewed as the signal of interest. The CS is first utilized as a preprocessing of FEKO, which modifies the conventional plane incident waves to the excitations that the CS needed. Then, FEKO is applied to solve the scattering problems under the new set of excitations to get the measurements of the scattered fields. Finally, the CS is secondly introduced as a postprocessing of FEKO, where CS inversion is employed to recover the desired far-zone multistatic scattered fields. To make a full use of the high efficiency and the deep optimization benefits of FEKO in solving wide-angle scattering problems, two forms of measurement matrixes are introduced, which have a more concise expression, and can reduce the simulating runtimes dramatically. The multistatic scattering radar cross section for different objects obtained from CS-FEKO are presented and compared with those derived from FEKO to illustrate the accuracy and efficiency of the proposed method. [ABSTRACT FROM PUBLISHER]

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]

This paper presents a novel formulation of the source reconstruction problem that aims at increasing the accuracy of near-field (NF) to far-field (FF) transformations in a particular measurement arrangement, where the NF data are rapidly acquired by a planar array of H-field probes located close to a ground plane. A source reconstruction algorithm is proposed for obtaining the near electric and magnetic fields as well as the FF radiation pattern of the antenna under test after filtering the effects of the currents induced on the ground plane backing the probe array. This algorithm exploits a system of integral equations that, after discretization according to the method of moments, enables backprojecting the measured fields on equivalent sources distributed over an arbitrary 3-D surface. Different integral equations are considered for that purpose. The accuracy provided by four different integral formulations is investigated from measured and synthetic experimental data and compared with the standard plane wave spectrum reconstruction technique, making it possible to arrive at a conclusion as to which one to use in order to make the final analysis. [ABSTRACT FROM PUBLISHER]

In this paper, we elaborate the method to successively find higher order terms of the asymptotic expansion of the field diffracted at a thin dielectric layer in 2-D problems (both the cases of E- and H-polarization). Each iteration of this method can be reduced to some standard 1-D boundary problem with a second-order differential equation and boundary conditions of impedance type. The boundary problem solvability and uniqueness are studied. The derivation of the leading asymptotic term is described, along with its geometrical optics meaning. The structure of the second asymptotic term is studied and analyzed with respect to its partial terms. Special attention is given to the partial terms describing the contribution to the diffracted field of the curvature of boundaries and their mutual slope. The results are verified by comparison with a solution obtained with the integral equation method. [ABSTRACT FROM PUBLISHER]

A new single-source integral equation is proposed for the solution of electromagnetic wave scattering problems. The traditional volume electric field integral equation is reduced to the new single-source surface integral equation by representing the electric field inside the scatterer as a superposition of spherical waves emanating from its boundary. Such new integral equation formulation has been previously developed for the scalar and vector cases of 2-D scattering problems. In this paper, the 3-D form of this new single-source surface integral equation for scattering on homogeneous nonmagnetic dielectrics is proposed. Detailed description of the method of moments (MoMs) discretization and its resultant matrices is presented. In order to validate the new integral equation formulation and verify the accuracy of its MoMs discretization, its solution is compared against the analytical Mie series solution and fields computed using the commercial electromagnetic analysis software. [ABSTRACT FROM PUBLISHER]