A fast combined field volume integral equation solution to EM scattering by 3-D dielectric objects of arbitrary permittivity and permeability

A fast solution to the combined field volume integral equation (CFVIE) for electromagnetic scattering by large three-dimensional dielectric bodies of arbitrary permittivity and permeability is presented. The CFVIE is formulated in the region of the scatterers by expressing the total fields as the sum of the incident wave and the radiated wave due to both the electric and magnetic polarization currents. The resultant integral equation is solved using the method of moments (MoM). Then the precorrected fast Fourier transform (P-FFT) method is applied to reduce the memory requirement and accelerate the matrix-vector multiplication in the MoM solution. In the implementation of the P-FFT method, two sets of projection operators are constructed respectively for the projections of the electric sources and magnetic sources. In addition, two sets of interpolation operators are also applied respectively for the computation of the vector/scalar potentials and the curl of the vector potentials in the support of the testing functions. The resultant method has a memory requirement of O(N) and a computational complexity of O(NlogN) respectively, where N denotes the number of unknowns.     

Moment method analysis of the magnetic shielding factor of aconducting TM shield at ELF

This paper presents an integral equation and method of moments (MoM) solution to the problem of TM transmission by a metallic conducting shield at extremely low frequencies (ELF). In order to accurately compute the total fields interior to the shield, equivalent problems are formulated which avoid the numerically difficult problem of computing the total fields as the sum of the incident plus scattered fields. In particular, the total electric field on the interior surface of the shield is obtained by a volume current equivalent problem, and then the total magnetic field interior to the shield is formulated in terms of equivalent magnetic surface currents flowing on the interior surface of the shield replaced by a perfect conductor     

Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body

The method of moments technique for analyzing electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body is presented based on the combined field integral equations. The body is assumed to be illuminated by a plane wave. The surface equivalence principle is used to replace the body by equivalent electric and magnetic surface currents. These currents radiating in unbounded free space produce the correct scattered field outside. The negatives of these currents produce the correct total internal field, when radiating in an unbounded chiral medium. By enforcing the continuity of the tangential components of the total electric and magnetic fields on the surface of the body, a set of coupled integral equations is obtained for the equivalent surface currents. The surface of the body is modeled using triangular patches. The triangular rooftop vector expansion functions are used for both equivalent surface currents. The coefficients of these expansion functions are obtained using the method of moments. The mixed potential formulation for a chiral medium is developed and used to obtain explicit expressions for the electric and magnetic fields produced by surface currents. Numerical results for bistatic radar cross sections are presented for three chiral scatterers - a sphere, a finite circular cylinder, and a cube.     

Electromagnetic scattering from dielectric bodies

Far-field results obtained by two different methods are compared for the problem of electromagnetic scattering from dielectric objects. The two methods are the surface integral formulation, utilizing equivalent electric and magnetic surface currents, and the volume formulation, utilizing the equivalent electric polarization current. Triangular patches are used in the surface formulation and cubical cells are used in the volume formulation. The far-scattered fields obtained by the two methods are in good agreement, thereby validating both the approaches for the analysis of scattering problems. Numerical problems associated with the fields in the source region are also addressed     

An Efficient Volume Integral Equation Solution to EM Scattering by Complex Bodies With Inhomogeneous Bi-Isotropy

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.     

Single integral equation for electromagnetic scattering bythree-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation     

金属-各向异性介质体组合目标频域体表积分方程矩量法

利用体表积分方程矩量法求解了具有任意的介电常数张量和磁导率张量的各向异性介质与金属的组合目标的电磁散射问题.给出了基于RWG面基函数和SWG体基函数的体表积分方程阻抗矩阵元素表达式并详细推导了阻抗矩阵元素所涉及的各种积分运算的计算方法;通过数值计算实例与解析解或其它数值方法的详细对比分析,证明了计算公式的正确性.     

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.      

Studies on Fast Algorithm for the Scattering of a Large Array of Waveguide-Fed Wide-Slot Antennas in Millimeter Wave Region

We present an effective numerical technique to characterize the scattering of wide-slot antennas fed by waveguides with arbitrary terminations in terms of the method of moment (MoM) and the mixed potential integral equation (MPIE). In particular, the precorrected-fast Fourier transform (P-FFT) eliminates the need to generate and store the usual square impedance matrix andthus leads to speed up the matrix-vector multiplication in the resultant system. This property makes the Rao-Wilton-Glisson (RWG) functions to be useful in simulating electrically large-scale problems. In addition, the scattering from the finite ground surfaces is accounted for in the total scattered field by using the method of equivalent edge currents. The numerical results are presented and compared with both the traditional method of moment results obtained using the entire-domain basis functions and the experimental results, to demonstrate the proposed method to be a good candidate for study on the scattering of arbitrary wide-slot large array.     

Scattering from multiple conducting and dielectric bodies ofarbitrary shape

A simple moment-method solution is presented for the problem of electromagnetic scattering from structures consisting of multiple perfectly conducting and dielectric bodies of arbitrary shape. The system is excited by a plane wave. The surface equivalence principle is used to replace the bodies by equivalent electric and magnetic surface currents, radiating into an unbounded medium. A set of coupled integral equations, involving the surface currents, is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the bodies are approximated by planar triangular patches, and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. Results for the scattering cross sections are presented. The computed results are in very good agreement with the exact solutions and with published data     

Scattering by a chiral cylinder of arbitrary cross section

An integral equation and method-of-moments (MM) solution to the problem of scattering by an inhomogeneous chiral cylinder of arbitrary cross section is presented. The volume equivalence theorem for chiral media is developed and used to formulate a set of coupled integral equations for the electric and magnetic volume polarization currents representing the chiral cylinder. These coupled integral equations are solved using a standard pulse basis and point-matching MM solution. Numerical results, including echo width and internal fields, are presented for the scattering by chiral slabs and circular cylinders. These results are compared to exact solutions when available     

Electromagnetic Scattering by Arbitrarily Shaped PEC Targets Coated with Anisotropic Media Using Equivalent Dipole-Moment Method

The equivalent dipole-moment method (EDM) is extended and applied in the analysis of electromagnetic (EM) scattering by arbitrarily shaped perfect electric conductor (PEC) targets coated with electric anisotropic media in this paper. The scattering targets are discretized into tetrahedral volume elements in the material region and into triangle patches on the conducting surface, where the volume-surface integral equation (VSIE) is set up. Then the method of moments (MoM) is employed to solve the VSIE. In the impedance matrix, the near field interaction elements are computed by the conventional MoM while the far field interaction elements are modeled by the EDM. The proposed approach is sufficiently versatile in handling arbitrarily shaped objects coated with general electric anisotropic media and is easily constructed through a simple procedure. Numerical results are given to demonstrate the accuracy and efficiency of this method.     

Radiation and scattering from infinite periodic printed antennaswith inhomogeneous media

The hybrid method of moments (MoM)/Green's function method technique is applied to infinite periodic printed antenna arrays containing dielectric inhomogeneities. The solution uses an integral equation for an infinite periodic printed array on or over a homogeneous dielectric substrate, coupled with equivalent volume polarization currents for dielectric inhomogeneities on top of the homogeneous substrate. Volume pulse-basis functions were used to expand the volume polarization currents. A hybrid MoM/Green's function method solution was then obtained through the matrix form of the problem. The two-dimensional (2-D) solution of plane wave scattering from a grounded dielectric slab was used to validate the reaction impedance of the dielectric inhomogeneity. Several infinite periodic printed dipole arrays with dielectric supports and overlays were studied with this solution and good agreement was observed between the hybrid MoM/Green's function method and waveguide simulator experiments     

Electromagnetic scattering from arbitrary shaped conducting bodiescoated with lossy materials of arbitrary thickness

A simple and efficient numerical technique is presented to solve the electromagnetic scattering problem of coated conducting bodies of arbitrary shape. The surface equivalence principle is used to formulate the problem in terms of a set of coupled integral equations involving equivalent electric and magnetic surface currents which represent boundary fields. The conducting structures and the dielectric materials are modeled by planar triangular patches, and the method of moments is used to solve the integral equations. Numerical results for scattering cross sections are given for various structures and compared with other available data. These results are proved accurate by a number of representative examples     

Rigorous Analysis of Rectangular Dielectric Resonator Antenna With a Finite Ground Plane

A probe-fed rectangular dielectric resonator antenna (RDRA) placed on a finite ground plane is numerically investigated using method of moments (MoM). The whole structure of the antenna is exactly modeled in our simulation. The feed probe, coaxial cable and ground plane are modeled as surface electric currents, while the dielectric resonator (DR) and the internal dielectric of coaxial cable is modeled as volume polarization currents. Each of the objects is treated as a set of combined field integral equations. The associated couplings are then formulated with sets of integral equations. The coupled integral equations are solved using MoM in spatial domain. The effects of ground plane size, air gap between dielectric resonator and ground plane, probe length, and position on the radiation performance of the antenna including resonant frequency, input impedance, radiation patterns, and bandwidth are investigated. The results obtained for the antenna parameters based on the MoM investigation shows that there is a close agreement with those obtained by measurement. Moreover it is shown that the MoM results are more accurate than other simulation results using software package such as High Frequency Structure Simulator (HFSS).      

A comparison between two kinds of equivalent currents to analyze conducting bodies with apertures using moment methods: Application to horns with symmetry of revolution

A system of integral equations (SIE) based on the unique-hess theorem that uses only electric equivalent currents (EEC) is formulated to analyze conducting bodies with apertures. This SIE is compared with an SIE that uses both electric and magnetic equivalent currents (EMEC). In general, to solve both SIE's numerically difficult computations of Cauchy principal-value integrals with highly singular kernels are required. These integrals appear when computing electric (magnetic) fields created by magnetic (electric) currents. Their evaluation can be avoided using the EEC approach in many practical cases when the main interest is in the radiation patterns of aperture antennas. The two SIE's are compared by carrying out an analysis of rotationally symmetric horns using the moment method (MM) in its formulation for bodies of revolution. Numerical results of electric currents and radiation patterns are presented for small horns of various geometries. These results compare quite well with measurements for both SIE's. However, the central processing unit (CPU) time for the EEC formulation is an order of magnitude smaller than for the EMEC formulation.     

An improved near- to far-zone transformation for thefinite-difference time-domain method

Near- to far-zone transformation for the finite-difference time-domain (FDTD) method can be performed by integration of the equivalent electric and magnetic currents originating from scattered electric and magnetic fields on a surface enclosing the object. Normally, when calculating the surface integrals, either the electric or magnetic fields are averaged since the electric and magnetic fields are spatially shifted in the FDTD grid. It is shown that this interpolation is unnecessary and also less accurate than if an integration is performed on two different surfaces. It is also shown that the accuracy of the far-zone transformation can be further improved if the phase is compensated with respect to a second-order dispersion corrected wavenumber. For validation, scattering results for an empty volume, a circular disk, and a sphere are compared with analytical solutions     

TM scattering by a dielectric cylinder in the presence of a half-plane

The problem considered is the transverse magnetic (TM) scattering by a dielectric cylinder in the presence of a perfectly conducting half-plane. An integral equation, involving the half-plane Green's function in its Kernel, is obtained for the equivalent volume currents representing the dielectric cylinder. This integral equation is solved by the method of moments. Numerical results are compared with measurements for the echo width of a dielectric slab on a half-plane. The dielectric slab surface impedance and the fields inside the dielectric are also shown.     

Electromagnetic scattering interference between two shallow objects buried under 2-D random rough surfaces

A rigorous electromagnetic model has been used to analyze the scattering from two dielectric shallow objects buried under the two-dimensional (2-D) random rough ground (3-D scattering problem) as a means of predicting false alarms. The method of moments (MoM) accelerated by the steepest descent fast multipole method (SDFMM) is used to compute the equivalent electric and magnetic surface currents on all scatterers (i.e., the rough ground and the two buried objects). The roughness parameters influence the scattering interference mechanism of the two objects, however, a large separation distance (e.g., several correlation lengths) showed stronger effect for small ground roughness.     

Electromagnetic scattering from a chiral cylinder of arbitrarycross section

A simple moment solution is presented to the problem of electromagnetic scattering from a homogeneous chiral cylinder of arbitrary cross-section. The cylinder is assumed to be illuminated by either a TE or a TM wave. The surface equivalence principle is used to replace the cylinder by equivalent and magnetic-surface currents. These currents radiating in unbounded external medium produce the correct scattered field outside. When radiating in an unbounded chiral medium, they produce the correct total internal field. By enforcing the continuity of the tangential components of the total electric field on the surface of the cylinder, a set of coupled integral equations is obtained for the equivalent surface currents. Unlike a regular dielectric, the chiral scatterer produces both copolarized and cross-polarized scattered fields. Hence, both the electric and magnetic current each have a longitudinal and a circumferential component. These four components of the currents are obtained by using the method of moments (MoM) to solve the coupled set of integral equations. Pulses are used as expansion functions and point matching is used. The Green's dyads are used to develop explicit expressions for the electric field produced by two-dimensional surface currents radiating in an unbounded chiral medium. Some of the advantages and limitations of the method are discussed. The computed results include the internal field and the bistatic and monostatic echo widths. The results for a circular cylinder are in very good agreement with the exact eigenfunction solution