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A parity time-reversal duality symmetric structure constituted by a perfect electric conductor and perfect magnetic conductor (PMC) parallel plate waveguide is analyzed. This waveguide supports unimodal transverse electromagnetic (TEM) edge mode propagation protected against backscattering from a certain class of deformations and defects. The TEM solution is found in analytical form by using three different methods, namely, conformal mapping, mode-matching, and Fourier-transform methods. It is shown through numerical simulations that the mode propagation is robust with respect to deformations such as 90° bends and discontinuities such as transition to free space. Implementation of the PMC boundary conditions via both a bed of nails and a mushroom structure is also successfully investigated. [ABSTRACT FROM AUTHOR]

A new surface single-source integral equation (SSIE) is proposed for the solution of electromagnetic wave scattering problems in two dimensions. The traditional volume electric field integral equation (V-EFIE) is reduced to the new single-source surface integral equation by representing the electric field inside the scatterer as a superposition of cylindrical waves emanating from its boundary. While being rigorous in nature, the new single-source surface integral equation features half of the degrees of freedom compared with traditional surface integral equation formulations. It is amenable to derivative-free method of moments discretization as it features only electric-field-type of Green’s function instead of both electric and magnetic field Green’s functions. [ABSTRACT FROM AUTHOR]

A discretization of the impedance boundary condition electric field integral equation (IBC-EFIE) is introduced that: 1) yields the correct solution at arbitrarily small frequencies and 2) requires for its solution a number of matrix vector products bounded as the frequency tends to zero and as the mesh density increases. The low frequency stabilization is based on a projector-based discrete Helmholtz splitting, rescaling, and recombination that depends on the low frequency behavior of both the EFIE operator and the surface impedance condition. The dense mesh stabilization is a modification of the perfect electric conductor operator preconditioning approach taking into account the effect on the singular value spectrum of the IBC term. [ABSTRACT FROM AUTHOR]

We introduce a volume integral equation method for the numerical solution of the electromagnetic scattering problem from electrically anisotropic inhomogeneous objects. The problem’s unknown, that is the sum of the conduction and polarization current densities, is decomposed in terms of its loop, star and facet components. Suitable strategies have been implemented to enforce the uniqueness of this discrete representation. Furthermore, through a convenient scaling of the unknowns, we also make the present method immune to the low-frequency breakdown problem, showing its stability regardless of the operating frequency. This approach has been extensively validated against the null-field method by analyzing the scattering from a uniaxial dielectric sphere and a uniaxial dielectric slab and comparing the scattered electric field in both the near and far zones. The condition number of the scattering problem consisting of a slab with an assigned conductivity tensor is also monitored as a function of the exciting frequency. [ABSTRACT FROM AUTHOR]

The higher order method of moments (HOMoM) with a direct solver is hybridized with the multilevel fast multipole algorithm given the multiscale nature of airborne antenna arrays. The Poggio–Miller–Chang–Harrington–Wu formulation and the combined filed integral equation are solved for modeling metallic/dielectric antennas on a conducting platform. To accelerate the outer iteration between the two algorithms, the lower/upper decomposed matrix in HOMoM is reused and the initial values of current coefficients are properly set. Furthermore, a computational scheme based on the high-performance computing technique is designed to improve the hybrid method. A large model of a 2132-element microstrip array mounted on a 1020-wavelength airplane is accurately simulated. [ABSTRACT FROM PUBLISHER]

A novel integration approach is developed for efficiently evaluating double surface integrals in time-domain integral equation formulations. The approach mainly consists of an angular integration scheme for inner 2-D integrals and a modified outer integration scheme. The approach proposed can handle the singularity and near-hypersingularity of the 4-D integrals, and is sufficiently general for arbitrary types of basis functions over planar domains. As several numerical results will demonstrate, the proposed approach has high accuracy and rapid convergence rate for a variety of integral kernels. [ABSTRACT FROM PUBLISHER]

A hybrid multilevel fast multipole algorithm-physical optics algorithm is developed for the bistatic radar cross section computation of electrically large objects modeled with the impedance boundary condition. Surface integral equation formulation of the problem is based on the resonance free self-dual integral equation by Yan and Jin. Accuracy of the solutions of the developed methods is studied for various surface impedance values. [ABSTRACT FROM PUBLISHER]

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]

A new integral equation-based nonoverlapping domain decomposition method (NDDM) is proposed for analyzing electromagnetic (EM) scattering from electrically large PEC objects whose MLFMA models are too large for the user’s computer to accommodate. The integral equation is first built on the entire PEC surface, and the entire surface is partitioned into some nonoverlapping subsurfaces. The RWG functions are used to expand the surface current on the entire surface. Then, each full-RWG function across some boundary curve is split into two half-RWG functions whose unknown coefficients are constrained by the boundary current continuity (using the explicit boundary condition). The convergence of the outer-iterative scheme of the proposed NDDM is investigated theoretically and demonstrated to be very good, and hence a very large problem can be effectively solved in an ordinary computer. Some numerical examples are provided to demonstrate the correctness and robustness of the proposed method, and to compare the proposed method with the existing overlapping DDMs having similar attributes. [ABSTRACT FROM PUBLISHER]

A high-order Nyström scheme is developed for electromagnetic (EM) scattering problems of smooth objects. The implementation is based on different well-known charge-current formulations. This study aims to develop a novel quadrature scheme to compute different singular integrals that appear on integral equation methods in EMs. The proposed quadrature scheme is used on a locally corrected Nyström method, and applied to charge-current integral equations to obtain a fast, accurate, and a low-frequency stable method to solve EM scattering problems. The proposed method allows obtaining accuracy in the range 4–10 digits in the near electric and magnetic scattered field for certain simple geometries and a wide range of frequencies. We also do a preliminary research on nonsmooth geometries obtaining a certain degree of accuracy depending on the particular charge-current integral equation used. [ABSTRACT FROM PUBLISHER]

This communication presents a formulation that allows to use hierarchical basis preconditioners applicable to the electric field integral equation (EFIE) on multiply connected geometries without searching for global loops. Currently available hierarchical basis preconditioners need an explicit representation of global loops. Finding these requires a computational complexity exceeding the linearithmic complexity of fast matrix-vector multiplication methods. Instead of using an explicit representation of global loops, we utilize Helmholtz projectors to regularize the EFIE separately on the solenoidal, non-solenoidal, and harmonic Helmholtz subspaces. Thereby, we avoid the explicit recovery of the global loops and maintain the leading complexity of fast multiplication methods. Numerical results prove the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

We introduce a method to compress the impedance matrix of the method of moments (MoM) for the modeling of high-fidelity multiscale structures at low- to moderate-frequencies. We start from a method recently proposed to compress static (scalar) problems, proved to have O(N) computational complexity. We represent far coupling between groups through equivalent source distributions on properly defined, automatically generated equivalence surfaces. The equivalent sources are obtained via an inverse-source process that enforces equivalence of radiated fields on testing surfaces within a prescribed accuracy, and are intrinsically multiscale. This results in an O(N) complexity scaling of matrix-vector products, but reduces multiplicative constants (i.e., reduces time and memory requirements) for all structures. It affords an improved representation of couplings in multiscale structures, resulting in a fast convergence of iterative solvers. Our approach is Green's function independent and easy to be implemented in existing MoM codes; the present version is based on the electric field integral equation (EFIE). Numerical results prove the effectiveness of the proposed algorithm for complex multiscale structures. [ABSTRACT FROM PUBLISHER]

Limitations of the time-domain Leontovich impedance boundary condition are discussed for a canonical problem consisting of a planar interface with a conducting half-space. The exact analytical solution obtained using an extension of the Cagniard-DeHoop technique is presented and compared with the approximate one found via the impedance boundary concept. Ranges of applicability of the latter are introduced and numerically tested on illustrative examples. A proper understanding of these limitations may prove to be crucial in the emerging field of time-domain integral equation formulations in planar stratified media. [ABSTRACT FROM PUBLISHER]

This is the second of a two-part paper analyzing fundamental properties of the finite-gap generator when used as a feed in Hallén's and Pocklington's equations. Here, we examine more carefully the origin and nature of oscillations occurring with the approximate kernel and point out certain analogies to numerical phenomena within the method of auxiliary sources (MAS) and to physical phenomena such as superdirectivity and surface waves. We further provide a physical interpretation of the effective-current method (pertinent also to the delta-function generator) that widens the applicability of the method and explains a number of the theoretical findings in Part I. [ABSTRACT FROM PUBLISHER]

In this paper, we present a simple and efficient fully numerical technique for the evaluation of 4-D reaction integrals arising in the method of moments. In the proposed approach, the accuracy of the source integration, which uses a singularity cancellation scheme, is retained in the final 4-D reaction integral through the application of an appropriate variable transformation and numerical quadrature scheme to the test integral. Several numerical results compared to the usual Gauss–Legendre test quadrature demonstrate the accuracy of the method for both planar and curvilinear discretizations. Moreover, the proposed scheme is independent of test basis functions; hence, it can be used for higher order basis functions as well as curl-conforming or Buffa– Christiansen test basis functions. [ABSTRACT FROM PUBLISHER]

In this paper, a novel surface integral equation formulation is proposed to solve electromagnetic scattering from objects with impedance surfaces. Derived from a new implementation of the impedance boundary condition (IBC), the proposed surface integral equations are able to calculate scattering not only from objects with impedance surfaces, but also from perfect electric conductors (PEC) and perfect magnetic conductors (PMC) if the surface impedance is set to zero and infinity, respectively. By including both the surface electric and magnetic currents as unknown quantities, the proposed formulations are dual formulations of themselves, and are free of spurious interior resonance corruption. The condition numbers of the resulting system matrices with respect to different surface impedance and mesh densities, and applications to uniform and nonuniform cases are discussed. The multilevel fast multipole algorithm is employed for calculation of electromagnetic scattering from very large objects. Numerical examples are given to demonstrate the performance of the proposed formulations. [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]

To solve Hallén's integral equations accurately, Nyström method is applied in this paper. To obtain an exact and finite solution, both the exact kernel and a finite gap width must be taken into consideration in the case of a gap feed. A modification function that converts the approximate kernel to the exact kernel is derived. As the modification function is singular, a one-point correction method is proposed, as a singularity subtraction method. Using a step function source, we can use various quadrature rules to solve the problem. The results show small difference between them. The validity of this theory is confirmed by comparing the measured results and the calculated results. The effect of the feed system is shown to be strong. [ABSTRACT FROM PUBLISHER]

Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div- and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. [ABSTRACT FROM PUBLISHER]

In this paper, we present a purely numerical procedure to evaluate strongly near-singular integrals involving the gradient of Helmholtz-type potentials for observation points at finite, arbitrarily small distances from the source domain. In the proposed approach the source domain is subdivided into a disc plus truncated subtriangles, and proper variable transformations are applied in each integration domain to exactly cancel the kernel singularity. A novel feature of the proposed angular transform is that required discrete values of the inverse transform, which is transcendental, are determined via a root-finding procedure; the same idea can also be applied to other transforms that arise in singularity cancellation methods. The resulting integral may then evaluated via a low order Gauss-Legendre quadrature scheme. [ABSTRACT FROM PUBLISHER]

We present two new facet-oriented discretizations in method of moments (MoM) of the electric-magnetic field integral equation (EMFIE) with the recently proposed Taylor-orthogonal (TO) and divergence-Taylor-orthogonal (div-TO) basis functions. These new schemes, which we call stable, unlike the recently published divergence TO discretization of the EMFIE, which we call standard, result in impedance matrices with stable condition number in the very low frequency regime. More importantly, we show for sharp-edged objects of moderately small dimensions that the computed RCS with the stable EMFIE schemes show improved accuracy with respect to the standard EMFIE scheme. The computed RCS for the sharp-edged objects tested becomes much closer to the RCS computed with the RWG discretization of the electric-field integral equation (EFIE), which is well-known to provide good RCS accuracy in these cases. To provide best assessment on the relative performance of the several implementations, we have cancelled the main numerical sources of error in the RCS computation: (i) we implement the EMFIE so that the non-null static quasi-solenoidal current does not contribute in the far-field computation; (ii) we compute with machine-precision the strongly singular Kernel-contributions in the impedance elements with the direct evaluation method. [ABSTRACT FROM PUBLISHER]

Single-source time-domain electric- and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure, thus allowing for a marching-on-in-time (MOT) solution scheme. Unlike dual-source formulations, single-source equations involve space-time domain operator products, for which spatial discretization techniques developed for standalone operators do not apply. Here, the spatial discretization of the single-source time-domain integral equations is achieved by using the high-order divergence-conforming basis functions developed by Graglia alongside the high-order divergence- and quasi curl-conforming (DQCC) basis functions of Valdés The combination of these two sets allows for a well-conditioned mapping from div- to curl-conforming function spaces that fully respects the space-mapping properties of the space-time operators involved. Numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the MOT scheme. [ABSTRACT FROM PUBLISHER]

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

A fast wideband integral equation (IE) solver combining the multilevel interpolatory fast Fourier transform accelerated approach (MLIPFFT) with the multilevel fast multipole method (MLFMM) is discussed. On electrically fine levels within an oct-tree multilevel structure, coupling computations are performed by MLIPFFT. This method is based on a 3D Lagrange factorization of the pertinent Green's functions with a smooth approximation error in space and it does not suffer a low frequency breakdown as known from MLFMM. For high frequency integral equation problems, MLIPFFT has decreased computational efficiency as the Nyquist theorem requires increasing numbers of samples in 3 dimensions. Due to a transition from the interpolation point based MLIPFFT source/receive formulation towards an appropriate k-space representation at a certain level within the oct-tree, the high frequency efficient MLFMM can be employed for coarse levels. The hybrid algorithm is hence well suited for fast wideband integral equation solutions. Both, mixed-potential and direct-field formulations are considered. Furthermore, a method for MLIPFFT extrapolation error reduction based on fine level interpolation domain spreading is introduced. In several numerical examples, the performance of the proposed algorithm is demonstrated. [ABSTRACT FROM PUBLISHER]

A true domain decomposition method to obtain numerical solution involving electrically large bodies using the method of moments (MOM) formulation is the subject matter of the present work. The electrically large body is initially divided into smaller sub-structures. By defining a set of new basis functions adaptively, utilizing the primary basis functions, a solution scheme is developed which completely eliminates the interaction of one substructure with the rest of the body. This procedure enables to solve each substructure independently and involves no iterative solution as a final step. The present method is conceptually simple and applicable to any MOM solution. Further, the method can easily handle multiple right-hand side vectors much the same way as the conventional MOM solution. A few representative numerical examples are presented to illustrate the applicability of the new method. [ABSTRACT FROM PUBLISHER]

Volume integral equations (VIEs) are indispensable for solving inhomogeneous or anisotropic electromagnetic (EM) problems by integral equation approach. The solution of VIEs strongly relies on the discretization of volume integral domains, and tetrahedral elements in discretization are usually preferred for arbitrary geometric shapes. Unlike discretizing a surface domain, discretizing a volume domain is very inconvenient in practice, and special commercial software is needed in general even for a simple and regular geometry. To release the burden of descretizing volume domains, especially to remove the constraint of mesh conformity in the traditional method of moments (MoM), we propose a novel meshfree scheme for solving VIEs in this paper. The scheme is based on the transformation of volume integrals into boundary integrals through the Green–Gauss theorem when integral kernels are regularized by excluding a small cylinder enclosing the observation node. The original integral domain represented by the object is also expanded to a cylindrical domain circumscribing the object to facilitate the evaluation of boundary integrals. The singular integrals over the small cylinder are specially handled with singularity subtraction techniques. Numerical examples for EM scattering by inhomogeneous or anisotropic objects are presented to illustrate the scheme, and good results are observed. [ABSTRACT FROM PUBLISHER]

Scattering of time-harmonic electromagnetic waves by chiral structures can be modeled via an extension of the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) boundary integral equation for analyzing scattering by dielectric objects. The classical PMCHWT equation however suffers from dense discretization breakdown: the matrices resulting from its discretization become increasingly ill-conditioned when the mesh density increases. This contribution revisits the PMCHWT equation for chiral media. It is demonstrated that it also suffers from dense discretization breakdown. This dense discretization breakdown is mitigated by the construction of a Calderón multiplicative preconditioner. A stable discretization scheme is introduced, and the resulting algorithm's accuracy and efficiency are corroborated by numerical examples. [ABSTRACT FROM PUBLISHER]

A complete set of entire-domain basis functions are introduced for the analysis of scattering from bodies with curved surfaces; they are defined via the application of a generalization of the Shannon sampling theorem. These basis functions are defined for curved patches with arbitrary contours, via a three-step procedure. First, the curved patch is mapped, via Transformation Optics, onto a flat parametric domain surrounded by a virtual anisotropic inhomogeneous space. Next, linear-phase functions are defined on the parametric flat domain; the sufficient and non-redundant number of functions is found by using a spectral domain “completeness relationship” of the delta function. Finally, the back-transformation from flat anisotropic to curved isotropic space yields the basis functions for the curved patch. The number of basis functions so obtained matches the degrees of freedom of the field known in the literature. Numerical results show the effectiveness of the representation for both fields and currents. [ABSTRACT FROM PUBLISHER]

We present an algorithm for the fast and efficient solution of integral equations that arise in the analysis of scattering from periodic arrays of PEC objects, such as multiband frequency selective surfaces (FSS) or metamaterial structures. Our approach relies upon the method of Accelerated Cartesian Expansions (ACE) to rapidly evaluate the requisite potential integrals. ACE is analogous to FMM in that it can be used to accelerate the matrix vector product used in the solution of systems discretized using MoM. Here, ACE provides linear scaling in both CPU time and memory. Details regarding the implementation of this method within the context of periodic systems are provided, as well as results that establish error convergence and scalability. We also demonstrate the applicability of this algorithm by studying several exemplary electrically dense systems. [ABSTRACT FROM PUBLISHER]

The multiple-grid adaptive integral method (MG-AIM) is extended for fast analysis of scattering from piecewise homogeneous structures on or above a perfect electrically/ magnetically conducting plane. Because the Green functions in the relevant integral equations contain (i) reflection terms that are in correlation form in the direction normal to the plane and (ii) direct terms that are in convolution form in all directions, the MG-AIM propagation stage gives rise to Hankel-(two level) block-Toeplitz matrices in addition to the usual (three level) block-Toeplitz matrices. These additional matrices are multiplied with trial vectors during the iterative solution stage by using FFTs; however, to improve efficiency, the FFTs computed for multiplying the direct terms are recycled. Numerical examples show that the proposed method requires (almost) half the number of computations and storage space compared to a brute-force imaging scheme for structures that terminate on the plane; larger gains are observed for structures residing above the plane. [ABSTRACT FROM AUTHOR]

In analyzing conducting bodies composed of surfaces connected to wires via a method of moments discretization of the electric field integral equation, junction basis functions are defined at connection points between wires and surfaces to correctly capture the physics of the current flux in the vicinity of the junction. In evaluating the associated self-term vector potential surface integrals, two singularities are present: one is related to the Green's function, and the other is due to the 1/\rho behavior of the junction basis function that models the current near a junction. Here we present a simple and efficient numerical procedure for evaluating singular and near-singular source vector potential integrals involving junction basis functions. The approach is based on a double transformation that cancels both singularities and also overcomes some limitations of singularity subtraction methods. The proposed scheme is then optimized to obtain at least four correct digits in the evaluation of these integrals. Essentially arbitrary accuracy is achievable by suitably increasing the quadrature order. [ABSTRACT FROM AUTHOR]

A new method for solving the time-domain integral equations of electromagnetic scattering from dispersive dielectric bodies is proposed. The method is based on the finite difference delay modeling scheme, which accomplishes the temporal discretization by substituting a z-domain finite-difference approximation for the continuous time Laplace domain parameter. The inverse z-transform used for computing the temporal kernels is calculated numerically using the trapezoidal rule and inverse discrete Fourier transform. Arbitrary dispersive models can be simulated without extraneous convolution using the new technique. The normal field equations are augmented to the standard tangential equations to solve the low-frequency instability problem. [ABSTRACT FROM AUTHOR]

The application of integral equations for the frequency domain analysis of scattering problems requires the accurate evaluation of interaction integrals. Generally speaking, the most critical integral is the selfpatch. However, due to the non-smoothness of the Green function, this integral is also the toughest to calculate numerically. In previous work, the source and test integrals have been determined analytically for the 1/R singularity, i.e., the static kernel. In this work we extend this result to the terms of the form Rn, ∀n ε {0, 1, 2, 3, 4} that occur in the Taylor expansion of the Green function. Numerical testing shows that truncating the Taylor series beyond n= 4 yields a highly accurate result for λ/7 and λ/10 discretizations. These analytical formulas are also very robust when applied to highly irregular triangles. [ABSTRACT FROM AUTHOR]

The volume integral equations (VIEs) for electromagnetic (EM) scattering by three-dimensional (3D) penetrable objects are solved by Nyström method. The VIEs are essential and cannot be replaced by surface integral equations (SIEs) for inhomogeneous problems, but they are usually solved by the method of moments (MoM). The Nyström method as an alternative for the MoM has shown much promise and has been widely used to solve the SIEs, but it is less frequently applied to the VIEs, especially for 3D EM problems. In this work, we implement the Nyström method for 3D VIEs by developing an efficient local correction scheme for singular and near singular integrals over tetrahedral elements. The scheme first interpolates the unknown functions within the tetrahedral elements and then derives analytical solutions for the resultant singular or near singular integrals after singularity subtraction. The scheme is simpler and more efficient in implementation compared with those based on the redesign of quadrature rules for the singular or near singular integrands. Numerical examples are presented to demonstrate the effectiveness of the proposed scheme and its convergence feature is also studied. [ABSTRACT FROM AUTHOR]

A multiple-grid extension of the adaptive integral method (AIM) is presented for fast analysis of scattering from piecewise homogeneous structures. The proposed scheme accelerates the iterative method-of-moments solution of the pertinent surface integral equations by employing multiple auxiliary Cartesian grids: If the structure of interest is composed of K homogeneous regions, it introduces K different auxiliary grids. It uses the kth auxiliary grid first to determine near-zones for the basis functions and then to execute AIM projection, propagation, interpolation, and near-zone pre-correction stages in the kth region. Thus, the AIM stages are executed a total of K times using different grids and different groups of basis functions. The proposed multiple-grid AIM scheme requires a total of O (Nnz,near + Σk NkC log NkC) operations per iteration, where Nnz,near denotes the total number of near-zone interactions in all regions and NkC denotes the number of nodes of the kth Cartesian grid. Numerical results validate the method's accuracy and reduced complexity for large-scale canonical structures with large numbers of regions (up to ~ 106 degrees of freedom and ~ 103 regions). Moreover, an investigation of HF-band wave propagation in a loblolly pine forest model demonstrates the method's generality and practical applicability. Multiple-grid AIM accelerated simulations with various tree models show that higher fidelity models for the trunk material and branch geometry are needed for accurate calculation of horizontally-polarized field propagation while lower fidelity models can be satisfactory for analyzing vertically-polarized field propagation. [ABSTRACT FROM AUTHOR]

Electromagnetic scattering is investigated for an arbitrarily shaped bi-isotropic body of revolution. The surface equivalent principle is applied to represent the electromagnetic fields inside bi-isotropic material in term of equivalent surface electric and magnetic currents, and a field decomposition method is introduced to simplify the handling of these equivalent surface currents. By enforcing boundary condition, a set of coupled surface integral equations is established. Incorporated by Galerkin procedure, Method of Moment is used to solve this set of equations. To utilize the rotational symmetry of body of revolution, the equivalent surface currents are expanded in term of Fourier series, and then expanded in terms of triangular basic function. The solution is implemented with a computer program written in Fortran language. To validate this solution, bistatic radar cross section of scattering by two different bi-isotropic scatters are presented, and good agreement is found. [ABSTRACT FROM AUTHOR]

Differences between certain solvable and nonsolvable ill-posed integral equations, with the same nonsingular kernel, are discussed. The main results come from constructing a solvable equation in the context of straight thin-wire antennas. The kernel of this equation is the usual approximate (also called reduced) kernel, while its exact solution is the familiar sinusoidal current. Numerical solutions to this solvable equation are compared to corresponding numerical solutions of the usual--Hallén and Pocklington--equations with the approximate kernel; it is known from previous publications that these last two equations are nonsolvable and that their numerical solutions present severe oscillations when the number of basis functions is sufficiently large. It is found that the difficulties encountered in the former (solvable) equation are much less important compared to those of the nonsolvable ones. The same conclusion is brought out from other integral equations, arising in different contexts (thin-wire circular-loop antenna, Method of Auxiliary Sources, and straight wire antenna of infinite length). We discuss the consistency of our results with Picard's theorem. The results in this paper supplement previous publications regarding the difficulties of numerically solving thin-wire integral equations with the approximate kernel. [ABSTRACT FROM AUTHOR]

A novel approach of dual GPOF (general pencil of functions) combined with the DCIM (the discrete complex image method) is developed to accelerate the Sommerfeld integral evaluation, when the mixed potential integral equation (MPIE) is applied to numerically calculate scattering from a conductive object partially embedded in a dielectric halfspace, where the field and source points are located in different media. Firstly, the factors related with the field point are separated from the spectrum function, and the GPOF is used to find the complex image parameters at finite discrete source points. Secondly, the GPOF is used again to fit the functional relationship of each complex image parameter with the source positions to evaluate the complex image parameters for any source position in a closed functional summation. Comparing numerical results of dual GPOF and direct numerical integration, this dual GPOF process is proved highly effective. Finally, dual GPOF/DCIM is applied to computation of electromagnetic scattering from a PEC spherical object partially embedded in a dielectric half-space medium, and numerical scattering results upon different model parameters are presented and analyzed. [ABSTRACT FROM AUTHOR]

We consider electromagnetics problems involving composite geometries with coexisting open and closed conductors. Hybrid integral equations are presented to improve the efficiency of the solutions, compared to the conventional electric-field integral equation. We investigate the convergence characteristics of iterative solutions of large composite problems with the multilevel fast multipole algorithm. Following a thorough study of how the convergence characteristics depends on the problem geometry, formulation, and iterative solvers, we provide concrete guidelines for efficient solutions. [ABSTRACT FROM AUTHOR]

We consider fast and accurate solutions of scattering problems involving increasingly large dielectric objects formulated by surface integral equations. We compare various formulations when the objects are discretized with Rao-Wilton-Glisson functions, and the resulting matrix equations are solved iteratively by employing the multilevel fast multipole algorithm (MLFMA). For large problems, we show that a combined-field formulation, namely, the electric and magnetic current combined-field integral equation (JMCFIE), requires fewer iterations than other formulations within the context of MLFMA. In addition to its efficiency, JMCFIE is also more accurate than the normal formulations and becomes preferable, especially when the problems cannot be solved easily with the tangential formulations. [ABSTRACT FROM AUTHOR]

In connection with a high order method of moments solution of integral equations for electromagnetic scattering, several approaches are investigated for representing current and charge densities in the vicinity of corners. One approach uses the first N terms from the asymptotic solution for an infinite wedge to represent the current density. An alternative approach uses a traditional polynomial type of expansion, but augments it in the vicinity of corners with additional terms from the wedge result. The residual error obtained via the solution of an over-determined system of equations is used to judge the relative accuracy and efficiency of various approaches. [ABSTRACT FROM AUTHOR]

We study TM and TE diffraction by a perfectly conducting half-plane in presence of a perfectly conducting flat strip of finite width and infinite length; the edges of the strip are parallel to the edge of the half-plane. The relevant integral equations with unknowns the induced current densities on the strip are solved by a Nyström and a Galerkin method that fully account for the singular nature of the kernels and the singularities of the solution at the edges. The proposed algorithms are highly accurate, and appear to converge exponentially as shown by detailed numerical examples and case studies. The Nyström method is the most efficient of the two methods because of its simple formulation, fast computer implementation, and much less effort in computing the matrix elements. When the strip is coplanar to the half-plane, an additional formulation method in terms of equivalent surface magnetic currents is possible in the framework of the field equivalence principles. This alternative method is applied in order to validate the algorithms and test their accuracy. [ABSTRACT FROM AUTHOR]

The solution of scattering problems involving low-contrast dielectric objects with three-dimensional arbitrary shapes is considered. Using the traditional forms of the surface integral equations, scattered fields cannot be calculated accurately if the contrast of the object is low. Therefore, we consider the stabilization of the formulations by extracting the nonradiating parts of the equivalent currents. We also investigate various types of stable formulations and show that accuracy can be improved systematically by eliminating the identity terms from the integral-equation kernels. Traditional and stable formulations are compared, not only for small scatterers but also for relatively large problems solved by employing the multilevel fast multipole algorithm. Stable and accurate solutions of dielectric contrasts as low as 10-4 are demonstrated on problems involving more than 250000 unknowns. [ABSTRACT FROM AUTHOR]

Modified magnetic field integral equations (MFIEs) are proposed incorporating a testing integration in the direction normal to the boundary of the target surface. The result involves a simpler kernel than the conventional MFIE, facilitating accurate computations. By employing a complex exponential testing function, the equations can be made immune to the interior resonance problem. The influence of the limits of integration, and the overall accuracy, is investigated using high order basis functions. [ABSTRACT FROM AUTHOR]

A novel regularized combined field integral equation pertinent to the analysis of scattering from 2-D perfect electrically conducting objects is presented. The equation is immune from ill-conditioning due to dense spatial discretizations and appears free from internal resonances. The regularization is achieved via analytical inversion of the hypersingular part of the combined field integral equation, without negative repercussions on computational complexity. Numerical results are presented that show the effectiveness of the proposed formulation. [ABSTRACT FROM AUTHOR]

A generalized volume integral equation method is formulated for electromagnetic scattering by arbitrarily shaped complex bodies with inhomogeneous bi-isotropy. Based on the volume equivalence principle, the integral equations are represented in terms of a pair of coupled bi-isotropic polarized volume electric and magnetic flux densities. Reduction of the integral equations into the corresponding matrix equations is obtained using the method of moments (MoM) combined with the tetrahedral mesh. In the MoM solution, the three-dimensional solenoidal function is incorporated as the basis function defined over each tetrahedral element and the details of implementation, particularly the treatment of integral singularities, will be elucidated. The efficiency and accuracy of the proposed method are validated by illustratively supported examples. [ABSTRACT FROM AUTHOR]

Higher order symmetrical moments play an important role in wave propagation and scattering in random media, however it remains to be solved under strong fluctuations. In this paper, a modified Gaussian solution method is proposed for analytically solving the n-nth moment. After propagating through a random medium in the fully saturated regime, the higher order symmetrical moment of the received wave is the sum of products of the second moments, i.e., the Gaussian solution. In strong scattering regimes, the higher order symmetrical moment can be considered as a sum of the Gaussian solution and a non-Gaussian correction term, where the key issue is how to solve the derived equation of the correction term. Two methods are proposed, i.e., Green's function method and the Rytov approximation approach. Green's function method leads to a rigorous solution form, but it is complicated due to an integral equation. The approach using the Rytov approximation is found to be reasonable, as the correction is relatively small. [ABSTRACT FROM AUTHOR]

We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving closed conductors. We consider the solutions of relatively large scattering problems by employing the multilevel fast multipole algorithm. Accuracy problems of MFIE and CFIE arising from their implementations with the conventional Rao-Wilton-Glisson (RWG) basis functions can be mitigated by using the LL functions for discretization. This is achieved without increasing the computational requirements and with only minor modifications in the existing codes based on the RWG functions. [ABSTRACT FROM AUTHOR]

For the straight wire, modeled as a hollow tube, we establish a conditional equivalence relation between the integral equations with exact and reduced kernel. This relation allows us to examine the existence and uniqueness conditions for the integral equation with reduced kernel, based on a local argument. Further, we characterize the ill-posedness of integral equation with reduced kernel and we propose a regularization and filtering procedure to extend the range of this integral equation. [ABSTRACT FROM AUTHOR]

A novel technique, based on a spectral domain integral equation method with analytically derived characteristic basis functions, is introduced in this paper. It enables us to treat scattering problems from electrically large faceted bodies in a numerically rigorous and computationally efficient manner, in terms of both time and memory. The analytically derived characteristic basis functions include certain desirable features of the asymptotic schemes and are defined on subdomains that can be electrically large, not being bound to the typical discretization size of the conventional method of moments. By properly weighting through a Galerkin procedure the resulting electric field integral equation, the problem is reduced to a matrix equation having dimensions that do not depend on the size of the scatterer but only on its shape. Electrically large problems can be handled in a computationally efficient manner by using the proposed method since the associated matrix size is relatively small; moreover, all the reduced matrix elements are calculated in the spectral domain without evaluating any convolution products. [ABSTRACT FROM AUTHOR]