Diffraction of an H-polarized electromagnetic wave by a circular cylinder with an infinite axial slot

A comparison of three methods of solution for the problem of scattering and diffraction of a transverse electric (TE) polarized plane wave by an infinite circular cylinder having an infinite axial slot is presented. In one method of solution, the aperture field integral equation (AFIE) method, the fields in and around the cylinder are found from the apertureE-field and the Green's functions for the interior and exterior of a cylinder. In the other two methods, the fields are determined from the surface current, which is obtained by solution of theH-field integral equation (HFIE) or theE-field integral equation (EFIE). The field in the aperture of the cylinder is found from the three methods, and the advantages and disadvantages of each method of solution are discussed. In addition, it is also shown that for shell thickness less than 1/20 of a wavelength, the aperture fields do not differ signifcantly from those of an infinitely thin shell cylinder.     

Analysis of pyramidal horn antennas using moment methods

A hybrid numerical technique is developed for electrically large pyramidal horn antennas radiating in free space. A stepped-waveguide method is used to analyze the interior surfaces of the horn transition. The electric field integral equation (EFIE) is employed on the outer surfaces of the pyramidal horn including the radiating aperture. Meanwhile, the magnetic field integral equation (MFIE) is used on the aperture to relate the aperture fields and those in the horn transition The resultant hybrid field integral equation (HFIE) is solved numerically by the method of moments. This formulation is both accurate and numerically stable so that high-gain microwave pyramidal horns can be analyzed rigorously. Far-field radiation patterns, both computed and measured, are presented for three electrically-large X-band horn antennas. The comparisons demonstrate that this method is accurate enough to predict the fine pattern structure at wide angles and in the back region. Computed far-field patterns and aperture field distributions of two smaller X-band horns are also presented along with a discussion on the validity of the approximate aperture field distributions routinely used in the analysis and design of pyramidal horns     

Near-zone gain of 500 MHz to 2.6 GHz rectangular standard pyramidalhorns

Full-wave solutions to the problem of radiation by rectangular standard pyramidal horn antennas are presented. The radiation problem is formulated in terms of an electric field integral equation (EFIE), which is solved using the method of moments (MoM) for four rectangular standard pyramidal horns covering the frequency range from 500 MHz to 2.6 GHz. Results for the near-zone gains as a function distance from the aperture of the horn antenna are presented. A comparison is made with the analytical formula for the fields and near-zone gains     

A hybrid symmetric FEM/MOM formulation applied to scattering byinhomogeneous bodies of revolution

A new symmetric formulation of the hybrid finite element method (HFEM) is described which combines elements of the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) for the exterior region along with the finite element solution for the interior region. The formulation is applied to scattering by inhomogeneous bodies of revolution. To avoid spurious modes in the interior region a combination of vector and nodal based finite elements are used. Integral equations in the exterior region are used to enforce the Sommerfeld radiation condition by matching both the tangential electric and magnetic fields between interior and exterior regions. Results from this symmetric formulation as well as formulations based solely on the EFIE or MFIE are compared to exact series solutions and integral equation solutions for a number of examples. The behaviors of the symmetric, EFIE, and MFIE solutions are examined at potential resonant frequencies of the interior and exterior regions, demonstrating the advantage of this symmetric formulation     

Scattering and coupling properties of a slotted elliptic cylinder

Near-field analysis and coupling of a perfectly conducting slotted elliptic cylinder excited by an electric line source placed inside or outside the cylinder is considered. The solution can be easily extended to account for a z-polarized incident plane wave excitation. The separation of variables technique is used to express external and internal fields in terms of Mathieu and modified Mathieu functions with unknown expansion coefficients. The problem is then reduced to an integral equation in terms of the aperture field. The solution of the integral equation is carried out by expressing the aperture field in terms of a Fourier series expansion with unknown coefficients. Then Galerkin's technique is introduced to solve for the unknown aperture field coefficients. Results for the penetrated and near fields are given in terms of different parameters such as location and type of the excitation, aperture width, cylindrical axial ratio, and the loading of the cylinder     

Near-zone gain of open-ended rectangular waveguides

Full-wave solutions to the problem of radiation by open-ended rectangular waveguides (OEG) are presented. The radiation problem is formulated in terms of an electric field integral equation (EFIE). The EFIE is solved using the method of moments for three OEG antennas covering the frequency range from 200 to 750 MHz. Results for the near-zone gains as a function of both frequency and distance from the OEG aperture are presented. Estimates for uncertainties in the calculated gain are also given     

Transient scattering by conducting surfaces of arbitrary shape

The time-domain electric field integral equation (EFIE) is used along with the method of moments to develop a simple and efficient numerical procedure for treating problems of transient scattering by arbitrary shaped conducting objects. The conducting surface is modeled by planar triangular patches for numerical purposes. Because the EFIE is used in the solution procedure, the method is applicable to both open and closed bodies. the EFIE approach is applied to the scattering problems of Gaussian plane wave illumination of a flat square plate and sphere. Comparisons of surface current densities and far-scattered fields are made with previous computations and good agreement is obtained in each case     

Finite-difference approach to the solution of time-domain integralequations for layered structures

A numerical algorithm for the analysis of transient electromagnetic fields in planar structures is proposed based on the time-domain magnetic-field integral equation (MFIE), electric-field integral equation (EFIE), and the marching-on-in-time approach. The field vectors are represented in terms of vector potential functions which are calculated either by integration or by the three-dimensional (3-D) wave equation according to the geometry of the structure. Thus, the algorithm combines the advantages of integral equation techniques and finite-difference schemes. While this approach is applicable to any geometries, it is especially suitable for multilayered planar structures and is competitive to the finite-difference time-domain (FDTD) method in the case of open and radiating problems. Theoretical results are verified by the analysis of a pulse propagation in a homogeneous open-end microstrip line     

Electromagnetic Scattering From Arbitrarily Shaped Dielectric Bodies Using Paired Pulse Vector Basis Functions and Method of Moments

A pair of orthogonal pulse vector basis functions is demonstrated for the calculation of electromagnetic scattering from arbitrarily-shaped material bodies. The basis functions are intended for use with triangular surface patch modeling applied to a method of moments (MoM) solution. For modeling the behavior of dielectric materials, several authors have used the same set of basis functions to represent equivalent electric and magnetic surface currents. This practice can result in zero-valued or very small diagonal terms in the moment matrix and an unstable numerical solution. To provide a more stable solution, we have developed orthogonally placed, pulse basis vectors: one for the electric surface current and one for the magnetic surface current. This combination ensures strongly diagonal moment matrices. The basis functions are suitable for electric field integral equation (EFIE), magnetic field integral equation (HFIE), and combined field formulations. In this work, we describe the implementations for EFIE and HFIE formulations and show example results for canonical figures.      

Analysis of lightning-radiated electromagnetic fields in the vicinity of lossy ground

An antenna theory (AT) approach in the frequency domain is presented to compute electromagnetic fields radiated by a lightning return stroke. The lightning channel is modeled as a lossy-wire monopole antenna (a wire antenna with distributed resistance) energized by a current source at its base, and the ground is modeled as a lossy half-space. The method of moments is used for solving the governing electric field integral equation (EFIE) in the frequency domain. The resultant current distribution along the channel is used to calculate electromagnetic fields at different distances from the channel. All field components are evaluated using a rapid but accurate procedure based on a new approximation of Sommerfeld integrals. In contrast with the previous models, the approach proposed here is characterized by a self-consistent treatment of different field components in air or on the surface of a lossy half-space. It is shown that the omission of surface wave terms in the general field equations, as done in the perfect-ground approximation, can strongly affect model-predicted field components.     

On the determination of resonant modes of dielectric objects using surface Integral equations

Although surface integral equations have been extensively used for solving the scattering problem of arbitrarily shaped dielectric objects, when applied to the resonance problem, there are still some issues not fully addressed by the literature. In this paper, the method of moments with Rao-Wilton-Glisson basis functions is applied to the electric field integral equation (EFIE) for solving the resonance problem of dielectric objects. The resonant frequency is obtained by searching for the minimum of the reciprocal of the condition number of the impedance matrix in the complex frequency plane, and the modal field distribution is obtained through singular value decomposition (SVD). The determinant of the impedance matrix is not used since it is difficult to find its roots. For the exterior EFIE, the original basis functions are used as testing functions; for the interior EFIE, the basis functions rotated by 90/spl deg/ are used as testing functions. To obtain an accurate modal field solution, the impedance matrix needs to be reduced by half before SVD is applied to it. Numerical results are given and compared with those obtained by using the volume integral equation.     

Planar near-field to far-field transformation using an equivalentmagnetic current approach

An alternative method is presented for computing far-field antenna patterns from near-field measurements. The method utilizes the near-field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna, and these currents are used to ascertain the far fields. Under certain approximations, the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near-field measurements are made. An electric field integral equation (EFIE) is developed to relate the near fields to the equivalent magnetic currents. The method of moments is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient method, and in the case of a rectangular matrix, a least-squares solution for the currents is found without explicitly computing the normal form of the equation. Near-field to far-field transformation for planar scanning may be efficiently performed under certain conditions. Numerical results are presented for several antenna configurations     

Analysis of dielectric-resonator antennas with emphasis onhemispherical structures

An overview is given for the development of dielectric-resonator antennas. A detailed analysis and study of the hemispherical structure, excited by a coaxial probe or a slot aperture, is then given, using the dyadic Green's functions pertaining to an electric-current source or a magnetic-current source, located in a dielectric sphere. The integral equation for a hemispherical dielectric-resonator antenna (DRA), excited by either a coaxial probe or a slot aperture, is obtained. The integral equation is solved using the method of moments. The antenna characteristics, such as input impedance, radiation patterns, directivity, and efficiency, are computed numerically, around the resonant frequency of the TE₁₁₁ mode (the HEM₁₁ mode for cylindrical coordinates). The computed input impedance is compared with numerical and experimental data available in the literature     

Integral equation solution for analyzing scattering fromone-dimensional periodic coated strips

A set of integral equations based on the surface/surface formulation are developed for analyzing electromagnetic scattering by one-dimensional periodic structures. To compare the accuracy, efficiency, and robustness of the formulation, the electric field integral equation (EFIE), magnetic field integral equation (MFIE), and combined field integral equation (CFIE) are developed for analyzing the same structure for different excitations. Due to the periodicity of the structure, the integral equations are formulated in the spectral domain using the Fourier transform of the integrodifferential operators. The generalized-biconjugate-gradient-fast Fourier transform method with subdomain basis functions is used to solve the matrix equation     

三维矢量散射积分方程中奇异性的分析

本文研究了电场积分方程（ＥＦＩＥ）中被积函数奇异性的处理方法,特别是三维矢量散射分析中出现的高阶奇异性,给出了两种解决积分方程奇异性的数值方法。一种方法是计算Ｏ（１／Ｒ）阶奇异积分转移法,另一种方法是为解决Ｏ（１／Ｒ＾２）高阶奇异积分的数值计算问题的,它是通过排除一包含奇点的有限小块,而这一小块区域对积分的贡献为零,从而使积分方程在整个积分域变得数值可积。     

Scattering from irregular-edged planar and curved surfaces

An electric field integral equation (EFIE) formulation is used to describe the electromagnetic scattering from finite planar and curved perfect electrical conducting surfaces truncated by an irregular edge. The edge can have an arbitrary form if it satisfies certain differentiability requirements. Similarly, the generating curve describing the surface can be convex, concave, or a combination of both. An edge-dependent entire domain Galerkin expansion is used for the current variation along the surface in the direction of translation. A subdomain expansion is used along the orthogonal direction. The backscatter cross sections obtained from the method of moments are compared with experimental data     

Improved Electric Field Integral Equation (IEFIE) for Analysis of Scattering From 3-D Conducting Structures

In this paper, a novel improved electric field integral equation (IEFIE) is developed to achieve fast and accurate solution of electromagnetic scattering from 3-D conducting structures. By adding the principle value term of the magnetic field integral equation (MFIE) operator into the EFIE operator, a well-conditioned improved EFIE operator is constructed. To achieve a reasonable accuracy, several update steps for the current vector are required. A multilevel fast multipole algorithm (MLFMA) is also applied to accelerate the computation of matrix-vector multiplications in the iteration. The present method attains much faster convergence of iterations than traditional EFIE and much better accuracy of the solution than the traditional combined field integral equation, particularly for 3-D structures with open or sharp surfaces. Numerical results show the validity and efficiency of the present method.     

Stabilisation procedure for electric field integral equation

A stabilisation procedure for the electric field integral equation (EFIE) is developed which renders the EFIE stable with respect to the discretisation interval used to numerically solve the equation. Representative numerical examples are provided which demonstrate the effectiveness of the procedure     

Calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavity

An efficient numerical technique is presented for the calculation of induced electric currents on coupled wires and multiconductor bundles placed in an arbitrary shaped cavity and excited by an external incident plane wave. The method is based upon the finite-difference time-domain (FD-TD) formulation. The concept of equivalent radius is used to replace wire bundles with single wires in the FD-TD model. Then, the radius of the equivalent wire is accounted by a modified FD-TD time-stepping expression (based on a Faraday's law contour-path formulation) for the looping magnetic fields adjacent to the wire. FD-TD computed fields at a virtual surface fully enclosing the equivalent wire are then obtained, permitting calculation of the currents on the wires of the original bundle using a standard electric field integral equation (EFIE). Substantial analytical and experimental validations are reported for both time-harmonic and broad-band excitations of wires in free space and in a high-Qmetal cavity.     

Hierarchal vector boundary elements and p-adaption for 3-Delectromagnetic scattering

This paper describes the development of new vector boundary elements for solving electromagnetic (EM) scattering problems. The new elements are suitable for the magnetic field integral equation (MFIE), electrical field integral equation (EFIE), or the combination field integral equation (CFIE). The basis functions are assigned to the edges of an element, rather than to its nodes. The new element guarantees the continuity of the normal component of the surface current across element edges. Furthermore, the basis functions are hierarchical from linear to higher order, which enables one to use the new elements in a p-adaption scheme