A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies

A method for calculating the electromagnetic scattering from and internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies is presented. A volume integral equation is formulated and solved by using the method of moments. Tetrahedral volume elements are used to model a scattering body in which the electrical parameters are assumed constant in each tetrahedron. Special basis functions are defined within the tetrahedral volume elements to insure that the normal electric field satisfies the correct jump condition at interfaces between different dielectric media. An approximate Galerkin testing procedure is used, with special care taken to correctly treat the derivatives in the scalar potential term. Calculated internal field distributions and scattering cross sections of dielectric spheres and rods are compared to and found in agreement with other calculations. The accuracy of the fields calculated by using the tetrahedral cell method is found to be comparable to that of cubical cell methods presently used for modeling arbitrarily shaped bodies, while the modeling flexibility is considerably greater.     

A Procedure for Calculating Fields Inside Arbitrarily Shaped, Inhomogeneous Dielectric Bodies Using Linear Basis Functions with the Moment Method

A moment method for calculating the internal field distributions of arbitrarily shaped, inhomogeneous dielectric bodies is presented. A free-space Green's function integral equation is used with 3-D linear basis functions to describe the field variation within cells. Polyhedral volume elements are used to model the scatterer's curvature realistically without an excessive number of unknowns. A new testing procednre, called the modified Galerkin's method, is developed and used to obtain the matrix equations with less CPU time but greater accuracy. Calculated internal field distributions of dielectric spheres, spheroids, and a composite model of a rat are compared with other calculations and experimental data. The agreement is generally good.     

Transient electromagnetic scattering from dielectric objects using the electric field Integral equation with Laguerre polynomials as temporal basis functions

In this paper, we propose a time-domain electric field integral equation (TD-EFIE) formulation for analyzing the transient electromagnetic response from three-dimensional (3-D) dielectric bodies. The solution method in this paper is based on the Galerkin's method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated using a set of orthonormal basis function that is derived from the Laguerre functions. These basis functions are also used as the temporal testing functions. Use of the Laguerre polynomials as expansion functions for the transient portion of response enables one not only to handle the time derivative terms in the integral equation in an analytic fashion but also completely separates the space and the time variables. Thus, the time variable along with the Courant condition can be eliminated in a Galerkin formulation using this procedure. We also propose an alternative formulation using a different expansion of the magnetic current. The total computational cost for this new method is similar to that of an implicit marching-on in time (MOT)-EFIE scheme, even though at each step this procedure requires more computations. Numerical results involving equivalent currents and far fields computed by the two proposed methods are presented and compared.     

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     

Accurate determination of modes in dielectric-loaded cylindricalcavities using a one-dimensional finite element method

A unified approach is presented for calculating the resonant frequencies of all the modes in cylindrical cavities axisymmetrically loaded with dielectrics. In this method, the radial variations of the field components in the resonator are expressed in terms of first-degree finite-element polynomials, whereas the axial variations of the field components are approximated by trigonometric functions. To calculate the resonant frequencies, an H-vector variational formulation is employed and minimized with respect to the coefficients of the expanded field components. Spurious solutions which are inherent in the finite-element technique are effectively eliminated by means of a penalty term included in the variational expression, imposing a divergence-free magnetic field constraint. To show the capability of the method, resonant frequencies of several cylindrical cavities, including those loaded with dielectric rods and dielectric rings, were calculated. A mode chart is presented which can be used for designing certain multimode dielectric-loaded cavity filters. In contrast to other rigorous techniques reported in the literature, the present method is highly efficient when dielectrics are fully extended along the cavity length     

Study of mixed-order basis functions for the locally corrected Nystro/spl uml/m method

A high-order locally corrected Nystro/spl uml/m (LCN) method employing the mixed-order basis functions proposed by C$80al/spl iota/s$80kan and Peterson is presented for the electromagnetic scattering by targets composed of both dielectric and conducting bodies. An integral operator based on a combined field formulation for conducting surfaces and a Mu/spl uml/ller formulation for dielectric surfaces is used. It is found that for general scattering objects, mixed-order basis functions accelerate the convergence of the LCN solution, can eliminate spurious charges, and can significantly reduce the condition number of the impedance matrix.     

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.      

TD‐CFIE Formulation for Transient Electromagnetic Scattering from 3‐D Dielectric Objects

In this paper, we present a time domain combined field integral equation formulation (TD‐CFIE) to analyze the transient electromagnetic response from dielectric objects. The solution method is based on the method of moments which involves separate spatial and temporal testing procedures. A set of the RWG functions is used for spatial expansion of the equivalent electric and magnetic current densities, and a combination of RWG and its orthogonal component is used for spatial testing. The time domain unknowns are approximated by a set of orthonormal basis functions derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable makes it possible to handle the time derivative terms in the integral equation and decouples the space‐time continuum in an analytic fashion. Numerical results computed by the proposed formulation are compared with the solutions of the frequency domain combined field integral equation.     

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.     

Field Solution for Radial Waveguides with Annular Discontinuities

A method is established which gives the internal field of a radial waveguide in the presence of annular-type slots on the conducting walls or metallic scatterers inside the guide. The exciting field can have a general form, and the dielectric constant of the region could be lossy or lossless. To obtain a solution, the induced currents (magnetic current in case of slot-type discontinuity) over the scattering bodies are expanded into a finite series of suitable basis functions with unknown coefficients. The total number of these functions is directly related to the electrical dimensions of the scatterers. The complex coefficients are then obtained by employing the appropriate Green's functions and an application of the boundary conditions over the scattering bodies. The method is then applied to the probIem of coupling between two radials waveguides by annular slots on the common boundary. It is shown that in general, higher order modes have significant effect on the solution, and for a precise evaluation of the field their contribution must also be included.     

Unrelated illumination method for electromagnetic inversescattering of inhomogeneous lossy dielectric bodies

A method aimed at reconstructing the complex permittivities of inhomogeneous lossy dielectric bodies is proposed. The method is based on the principle that sufficient information about a dielectric body can be obtained from the scattered field when the body is illuminated by an incident field composed of unrelated components. The derivations of the formulas are presented, and some numerical examples are given. The accuracy of the results show that the method has great potential in electromagnetic inverse scattering and microwave imaging     

Electromagnetic scattering by a mixture of conducting and dielectric objects: analysis using method of moments

In this paper, the method of moments is employed to solve the combined field integral equation for characterizing electromagnetic scattering by large three-dimensional structures of arbitrary shape. Unlike those discussed in the literature, these structures consist of mixed conducting and homogeneous dielectric objects. To improve the matrix conditioning number, the basis functions used to represent magnetic currents are also chosen as the popular Rao-Wilton-Glisson functions, but are multiplied by a constant number. A Galerkin's procedure is implemented, i.e., the testing functions are chosen to be the same as the basis functions.     

Waves and Evanescent Fields in Rectangular Waveguides Filled with a Transversely Inhomogeneous Dielectric

A numerical-calculation method for rectangular waveguides containing a transversely inhomogeneous dielectric is presented. The method is not restricted to the cutoff case or to special inhomogeneities. The relative permittivity of the dielectric can be an arbitrary function of the cross-sectional coordinates. The electric-and magnetic-field strengths, the dispersion characteristics of the propagating modes, and the attenuation constants of the evanescent modes result from the solution of a matrix eigenvalue problem with typically 8000 matrix elements. Propagating and evanescent modes in a waveguide containing a longitudinal semicircular dielectric rod are calculated as examples. The accuracy of the calculation method is confirmed by measurements and by calculating a special example with an exactly known solution. The error of the field intensities is typically 5 percent; the error of the dispersion characteristics and of the attenuation constants is typically 0.5 percent.     

Analysis of transient scattering from composite arbitrarily shapedcomplex structures

A time-domain surface integral equation approach based on the electric field formulation is utilized to calculate the transient scattering from both conducting and dielectric bodies consisting of arbitrarily shaped complex structures. The solution method is based on the method of moments (MoM) and involves the modeling of an arbitrarily shaped structure in conjunction with the triangular patch basis functions. An implicit method is described to solve the coupled integral equations derived utilizing the equivalence principle directly in the time domain. The usual late-time instabilities associated with the time-domain integral equations are avoided by using an implicit scheme. Detailed mathematical steps are included along with representative numerical results     

Scattering by two-dimensional lossy, inhomogeneous dielectric andmagnetic cylinders using linear pyramid basis functions and pointmatching

A volume integral equation approach is used to calculate the scattering characteristics of lossy, inhomogeneous, arbitrarily shaped, two-dimensional dielectric and magnetic bodies. The scatterer is divided into triangular patches, which simulate curved and piecewise linear boundaries more closely than circular cylinder cells. Linear pyramid basis functions are employed to expand the unknown total electric field at the triangle nodes. The enforcement of the boundary conditions by point matching at the nodes converts the electric field integral equation to a matrix equation. Example cases are run and compared to previous moment methods and exact solutions, and this method shows good agreement. This method requires only one unknown per node in dielectric and magnetic material, which is a significant reduction in unknowns and matrix storage compared to traditional methods. By duality, this method can be used at either transverse electric or transverse magnetic polarization     

Axial slot antenna on dielectric-coated elliptic cylinder

The radiation properties of an axial slot antenna on a conducting elliptic cylinder with a homogeneous dielectric coating are investigated. In the dielectric coating and in the exterior free-space region the field is expanded in elliptic waves using the Mathieu functions. The Mathieu angular functions are employed as basis and testing functions to enforce the boundary conditions at the interface between the dielectric and the free-space regions. The equations of continuity at the boundary are solved by Galerkin's method. Numerical results are presented in graphical form for the transverse electric (TE) and transverse magnetic (TM) polarizations to illustrate the far-field radiation patterns, the gain versus coating thickness, and the aperture conductance versus coating thickness     

Transmission through dielectric-filled slots in a conductingcylindrical shell of arbitrary cross section: TE case

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are 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. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory     

Radiation and scattering from structures involving finite-sizedielectric regions

A full-wave approach is presented for calculating the scattered fields produced by structures that involve finite-size dielectric regions. The dielectric is first approximated by an array of interlocking thin-wall sections; the electric field boundary conditions are then applied through the use of appropriate surface impedances. Rooftop basis functions, chosen to represent the surface current, are appropriately placed on the thin-wall sections in such a way as to accurately represent the polarization current while preventing fictitious charge within the dielectric. Rooftop currents are also used to represent the current on any conductor that may be present. The matrix elements are calculated, depending upon the distance between the source and field locations, through a scheme that employs Taylor series expansions and point source approximations. The technique is applied to scattering from dielectric cubes and composite dielectric-conductor structures, and to radiation from microstrip structures. Numerical convergence and agreement with the literature are demonstrated     

A Galerkin moment method for the analysis of an insulated antennain a dissipative dielectric medium

A Galerkin moment method is employed to solve the problem of a dielectric-coated dipole antenna in a dissipative medium. Piecewise sinusoids are used as basis and testing functions. The dielectric coating is modeled by equivalent-volume polarization currents, which are simply related to the conduction current distribution. No additional unknowns are introduced, and the size of the moment-method matrix is the same as that for bare antennas. Exact and approximate formulas for the near electric field are derived. The computed results exhibit excellent agreement with those previously published for a symmetric, as well as an asymmetric insulated dipole. Compared to its existing competitors, the new method appears to be more general and computationally efficient