Showing papers in "Electromagnetics in 1990"

A Time-Domain, Finite-Volume Treatment for the Maxwell Equations

Abstract: For computation of electromagnetic scattering from layered objects, the differential form of the time-domain Maxwell's equations are first cast in a conservation form and then solved using a finite-volume discretization procedure derived from proven Computational Fluid Dynamics (CFD) methods 1 . The formulation accounts for any variations in the material properties (time, space, and frequency dependent), and can handle thin resistive sheets and lossy coatings by positioning them at finite-volume cell boundaries. The time-domain approach handles both continuous wave (single frequency) and pulse (broadband frequency) incident excitation. Arbitrarily shaped objects are modeled by using a body-fitted coordinate transformation. For treatment of complex internal/external structures with many material layers, a multizone framework with ability to handle any type of zonal boundary conditions (perfectly conducting, flux through, zero flux, periodic, nonreflecting outer boundary, resistive card, and lossy ...

A Three-Dimensional Modified Finite Volume Technique for Maxwell's Equations

Abstract: A modified finite volume method for solving Maxwell's equations in the time-domain is presented. This method, which allows the use of general nonorthogonal mixed-polyhedral grids, is a direct generalisation of the canonical staggered-grid finite difference method. Employing mixed polyhedral cells, (hexahedral, tetrahedral, etc.) this method allows more accurate modeling of non-rectangular structures. The traditional “stair-stepped” boundary approximations associated with the orthogonal grid based finite difference methods ate avoided. Numerical results demonstrating the accuracy of this new method are presented.

The “Interior Resonance” Problem Associated with Surface Integral Equations of Electromagnetics: Numerical Consequences and a Survey of Remedies

Abstract: It is well known that certain surface integral equations used to describe exterior electromagnetic scattering problems may not produce unique solutions if applied to closed geometries that also represent resonant cavities. This paper explores the numerical consequences of the uniqueness problem. The “interior resonance” problem and several proposed remedies are illustrated using the eigenvalues of the integral operators for circular cylinders. Although an eigenvalue of the continuous integral operator vanishes at a resonance frequency, discretization error may prevent the associated matrix eigenvalue from becoming appreciably small. Inaccurate results are due to an incorrect balance between the excitation and the small matrix eigenvalue near a resonance frequency.

The Finite-Difference Time-Domain Method for Numerical Modeling of Electromagnetic Wave Interactions

Abstract: This paper succinctly reviews the background and formulation of the finite-difference time-domain (FD-TD) method for numerical modeling of electromagnetic wave interactions with arbitrary structures. Selected 3-D results are given showing comparisons with both measured data and other numerical modeling approaches. An assessment is made of the present horizon of FD-TD modeling capabilities, and possible future directions.

Instabilities in Time Marching Methods for Scattering: Cause and Rectification

Abstract: The occurrence of exponentially increasing instabilities is a common feature of time-marching methods for solving an integral equation arising in a transient scattering problem. The cause of this instability is shown to be related to the interior resonances of the scatterer at which the corresponding frequency domain integral equation fails to have a unique solution. This type of instability is eliminated by an averaging process. The necessary modifications to any existing computer programs are trivial and increase computational cost by about 10%.

E-Field, H-Field, and Combined Field Solution for Arbitrarily Shaped Three-Dimensional Dielectric Bodies

Abstract: In this work, we present three sets of formulations viz. the electric field integral equation (EFIE) formulation, the magnetic field integral equation (MFIE) formulation, and the combined field integral equation (CFIE) formulation for analyzing the three dimensional homogeneous dielectric bodies Illuminated by an Incident plane wave. In the process of solving these equations, the dielectric object Is approximated by planar triangular patches. On the surface of each triangle, two orthogonal vector functions are defined to approximate the equivalent electric and magnetic currents. These two vector functions serve as basis functions In the solution of the integral equations using the method of moments. The solution procedure thus obtained Is simple, efficient and yields good results. Sample numerical results such as Induced equivalent electric and magnetic currents and far scattered fields are presented for the case of a dielectric sphere and cylinder using all three formulations. The results are co...

Modeling Scattering From and Radiation by Arbitrary Shaped Objects with the Electric Field Integral Equation Triangular Surface Patch Code

Abstract: PATCH is a frequency domain electromagnetic scattering code based on a method-of-moments solution to the Electric Field Integral Equation (EFIE). The numerical methods are based on an earlier version of the code. The present code has the following capabilities: computation of scattering from multiple bodies, treatment of multiple intersecting surfaces, use of symmetry planes to reduce the number of unknowns, treatment of surfaces with lumped and distributed impedance loads, and the capability for plane wave or voltage source excitation. A primitive mesh generator has been included to ease the problem of input data generation. The outputs of the code are the currents on the body, radiated fields, far fields, radar cross section, and Thevenin equivalent circuits. Furthermore, thin wires attached to conducting surfaces may be modeled by use of an equivalent thin strip.

Scattering by an Impedance Sphere Coated with a Chiral Layer

Abstract: The scattering of a plane, linearly polarized electromagnetic wave by a sphere on whose surface an impedance boundary condition holds, and that is covered with a concentric layer of chiral material, is considered. Exact, explicit expressions are derived for the scattered field coefficients. The co-polarized and cross-polarized components of the far backscattered field are determined and discussed. The value of this canonical problem as a benchmark for computer codes is pointed out.

Finite Element Methods for the Solution of RF Radiation And Scattering Problems

Abstract: This paper presents the methods and results of using partial differential equation techniques for the solution of RF radiation and scattering problems. Specifically, frequency domain finite elements coupled with absorbing boundary conditions are extensively covered. Two-dimensional and three-dimensional formulations and computational results are presented. The two-dimensional formulation uses standard finite elements with either the Engquist-Majda or Bayliss-Turkel absorbing boundary conditions. The three-dimensional formulation also uses absorbing boundary conditions and finite elements, however, new, non-standard finite element basis functions specifically developed for vector field problems are used. These vector finite element basis functions are known as “edge-elements.” [1]

Electromagnetic Computation Using Parametric Geometry

Abstract: Electromagnetic formulations are presented that fully utilize the curvilinear geometry information available in parametric geometry codes. These parametric geometry codes (surface patch codes) are in wide use and the formulations presented can be used with any of these geometry codes Independent of the differences between versions. The ultimate goal is a three dimensional moment: method surface formulation enabling computation for bodies composed of metallic and nonmetallic portions. This goal requires that both the magnetic field integral equation operator and the electric field integral equation operator be encoded. To facilitate the presentation of the parametric geometry formulation of these operators, the simpler parametric geometry formulation for the physical optics integral is first presented. Additional background material based on two dimensional analysis is presented to address issues of faceting versus curvilinear and basis function choice.

Numerical Solution of Boundary Integral Equations in Time-Harmonic Electromagnetic Scattering

Abstract: We study the numerical solution of the boundary integral equation formulation for the scattering of time-harmonic electromagnetic waves from infinite cylinders. For smooth boundaries of the cylinder cross section we describe a Nystro¨m, a collocation and a Galerkin method based on an approximation by trigonometric polynomials on an equidistant mesh. For smooth data in each of the three methods the convergence is exponential. From the three approaches the Nystro¨m method is the most efficient since it requires the least computational effort. For cross sections with corners we develop a Nystro¨m method on a graded mesh based on the idea of transforming the nonsmooth case to a smooth periodic case via an appropriate substitution. We conclude the paper with some considerations on the corresponding three dimensional problem.

The Design of Linear and Planar Arrays of Waveguide-Fed Longitudinal Slots

Abstract: A new design procedure for small arrays of waveguide-fed longitudinal slots is introduced. Unlike previous methods, this procedure does not require characterization of the radiating elements in terms of their equivalent circuit representations. Instead, the fundamental integral equations that describe the array are used directly. Mutual coupling between slots, including both internal and external effects, and the finite thickness of the waveguide wall, are included as integral parts of the development. The results of two case studies are presented to illustrate the improved accuracy of this method over earlier approaches.

A combined finite element-boundary element formulation for solution of two-dimensional problems via CGFFT

Abstract: A method for the computation of electromagnetic scattering from arbitrary two-dimensional bodies is presented. The method combines the finite element and boundary element methods leading to a system for solution via the conjugate gradient Fast Fourier Transform (FFT) algorithm. Two forms of boundaries aimed at reducing the storage requirement of the boundary integral are investigated. It is shown that the boundary integral becomes convolutional when a circular enclosure is chosen, resulting in reduced storage requirement when the system is solved via the conjugate gradient FFT method. The same holds for the ogival enclosure, except that some of the boundary integrals are not convolutional and must be carefully treated to maintain O(N) memory requirement. Results for several circular and ogival structures are presented and shown to be in excellent agreement with those obtained by traditional methods.

Parallel Computation Applied to Electromagnetic Scattering and Radiation Analysis

Abstract: We have been applying the computational power of parallel processing to the solution of large-scale electromagnetic scattering and radiation problems. Several analysis codes have been implemented on the Jet Propulsion Laboratory/California Institute of Technology Mark IIIfp Hypercubes. The first code to be implemented was the Numerical Electromagnetics Code (NEC-2) from Lawrence Livermore National Laboratory. At first we simply ported it to run in the parallel processing environment. Since that time, taking advantage of the large hypercube memory and fast computation. we have enhanced parallel NEC to permit iterative design and analysis. Three other codes, frequency domain finite elements, time domain finite difference, and frequency selective surfaces, have been largely or completely developed within this parallel processing environment. Because of the massive problem size of the typical electromagnetics problem, our work is an important influence in determining the development of hardware, syst...

Electromagnetic Scattering by Arbitrarily Shaped Two-Dimensional Perfectly Conducting Objects Coated with Homogeneous Anisotropic Materials

Abstract: Combined-field surface integral equations are applied to analyze electromagnetic scattering from coated perfectly conducting objects. The conducting core and the homogeneous anisotropic coating layers covering it are assumed to be two-dimensional and of arbitrary shape. Furthermore, individual layers of anisotropic material constituting the composite clad structure are allowed to have distinct medium tensor properties. Numerical solution of the resulting integral equations is facilitated by the method of moments. Equivalent surface currents on the metal core and the jacket surface are computed, and along with the corresponding radar cross section are presented for a variety of scattering geometries.

The Effect of Finite Conductivity on Frequency Selective Surface Behaviour

Abstract: Tbe scattering problem for a Frequency Selective Surface (FSS) consisting of an array of patches or a perforated screen is solved. Both penetrable and impenetrable materials with dyadic surface impedance are considered. The problem is formulated directly in the spectral domain where the relevant functional equation is obtained and solved by the Galerkin Method of Moment. Further, an interesting circuit interpretation of the functional equation allows to assess the role played in the scattering problem by the boundary conditions directly in circuit terms. Results which point out the influence of the surface impedance on the frequency response of FSS's are reported.

Polygonal Plate Modeling

Abstract: The paper presents an overview of an integral equation and method of moments (MM) solution to the problem of radiation and/or scattering from a three dimensional perfectly conducting body of general shape. The method is based upon a surface patch MM solution of the electric field integral equation for the surface currents representing the body. The shape of the body is described in terms of a number of polygonal plates, which are (automatically) further segmented into quadrilateral patches for the purpose of defining the MM surface patch modes. Examples are shown which illustrate the ability of the method to treat complex and realistic shapes.

Electromagnetic Field Representation in (Inhomogeneous) Isotropic Chiral Media

Abstract: A general theoretical approach to the electromagnetics of isotropic chiral media is presented. An electromagnetic field representation in terms of scalar Hertz potentials is obtained. The validity of this representation encompasses inhomogeneous media where the constitutive parameters of the chiral structures - permittivity, permeability and chirality - are functions of one coordinate. In the homogeneous case the corresponding electric and magnetic scalar Green's functions are calculated analytically thus constituting the field solution for dipole sources.

Radiation and Dispersion Effects from Frequency-Modulated (FM) Sources

Abstract: We consider the Far-zone field radiated bv a frequency-modulated (FM) source in open-ended circular waveguide. The source is uniformly distributed over the waveguide cross-section. Possible multimode effects are included. The radiated fields are derived from an eauivalent source in the aperture. Far-zone fields are first obtained in the frequency domain with time-domain results following through an inverse Fourier transform. Results are given first in standard time and frequency domain plots. These are followed by short-time Fourier transforms and spectrograms that clearly show frequency modulation effects from the source and from the dispersion inherent in the wave propagation.

Diffraction of a Plane Wave by a Strip Grating

Abstract: The solution of a canonical problem regarding the diffraction of a plane electromagnetic wave incident, with an arbitrary angle, upon a strip grating formed by infinitely long thin metallic ribbons is found. The formulation is given for any relation between the width of the ribbons and the width between the ribbons. The exact solution is obtained by using Wiener-Hopf techniques in the case of equal width of the ribbon and the spacing. The numerical values of the transmission and reflection coefficients can be evaluated in a simple manner to any desired accuracy. Plots are given for different angles of incidence in a certain frequency range. The closed form of the TE modes scattering matrix is also given.

Time-domain Green function corresponding to a time-harmonic point source in complex space.

Abstract: The time-domain counterpart of the scalar field arising from a time-harmonic point source in the complex space is derived. The solution corresponds to the complex-space source Green function, which...

Partial Differential Equation Methods for Solving the Problem of Electromagnetic Scattering from a Body of Revolution

Abstract: In this paper we discuss the use of a local boundary condition derived from Wilcox's expansion for the scattered fields to achieve mesh truncation for finite difference and finite element meshes. We review the method for the case of finite difference meshes and then show how it can be generalized for the case of a finite element mesh. We show how the finite element formulation can be developed without the use of a variational expression. We also present numerical results obtained using the finite element method.

Insertion Loss and Phase Shift Variations of Microwave Signals Passing Through Heated Tissues

Abstract: In this paper the dependence of microwave signal insertion loss and phase shift variations with respect to temperature inside tissues is investigated theoretically employing a two-layer sphere to model parts of the human body. A transmit-receive microwave link near or around a two-layer sphere is considered. The known variation of the permittivity and conductivity of tissues with respect to temperature is employed. An exact analytical solution is employed to investigate the variation of microwave attenuation and phase shift, when the electromagnetic waves are passing through tissues heated up to hyperthermic temperatures. The feasibility of developing a non invasive temperature measuring technique is examined.

Electric and Magnetic Dipole Radiation in a Random Medium

Abstract: Electric and magnetic dipole radiation are studied for a medium where random, small-scale inhomogeneities are confined to a spherical shell region. Numerical results are presented for both the far-field pattern and the total radiated power. When the random inhomogeneities are located in the near field of the source, an electric dipole radiates a larger incoherent field than a magnetic dipole because of the electric dipole's larger reactive electric field.

Analysis of the Pulse Propagation in a Nonlinear Dielectric Parabolic Profile Slab Waveguide

Abstract: The pulse propagation in a nonlinear dielectric slab waveguide with parabolic index of refraction is analysed by means of a discretized integral equation. A two dimensional field distribution is assumed inside the dielectric slab waveguide. First the Green's Function of the corresponding linear problem is obtained. Then by using the slowly varying envelope approximation an integral equation for the electric field distribution inside the waveguide is derived. In order to solve this integral equation, discretizations along the propagation axis and on the time axis are employed. This formulation leads to a very efficient algorithm for the numerical calculation of the slowly varying envelope of the electric field distribution. Numerical results are computed and presented in the single mode case of propagation for various envelope amplitude values.

An Improvement to Stevenson's Derivation of Integral Equations for Waveguide Slot Analysis

Abstract: Stevenson [1] used the scalar Green’s theorem to derive integral equations for the magnetic field everywhere in the guide. These integral equations involve convolutions of Green's functions with the tangential electric fields in the slot.In the derivation of these equations it was assumed that the fields were continuous and had continuous derivatives everywhere inside the guide including the slot. However, once the equations were written purely in terms of the tangential electric fields only, these continuity requirements were dropped. The change in assumptions during the analysis causes the final integral equation to be incompatible with the previously derived equations. This paper presents an analysis which does not use these continuity assumptions and so is self consistent. Another assumption that Stevenson made and which is not necessary is the requirement that the fields decay to zero at ±∞.