Showing papers on "Computational electromagnetics published in 1993"

Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering

Abstract: The Born and Rytov approximations, widely used for solving scattering problems, are of limited utility for low-frequency electromagnetic scattering in geophysical applications where conductivity can vary over many orders of magnitude We present four new, relatively simple nonlinear estimators that can be used for rapid electromagnetic modeling The first, termed the static localized nonlinear approximation, is designed specifically to correct the magnitude of the electric field internal to the scatterer The second, termed the localized nonlinear approximation, improves the estimate of the phase of the scattered field and includes some of the cross-polarization effects due to full wave scattering Two further new estimators, based on the Rytov transformation (the localized nonlinear Rytov and the static localized nonlinear Rytov approximations) are designed to further improve the estimation of the phase of the scattered field, especially at high frequency and for larger size scatterers Although these approximations are nonlinear functions in conductivity, they are generally much faster to compute than the full forward problem, and are almost as efficient as the Born or Rytov approximations Moreover, the enhanced accuracy of the new estimators has made us optimistic about their application to low-frequency three-dimensional inverse problems in electromagnetics The approximations developed in this paper will also be applicable to fields such as quantum mechanics, optics, ultrasonics, and seismology

Benchmark radar targets for the validation of computational electromagnetics programs

Abstract: Results are presented of a set of computational electromagnetics validation measurements referring to three-dimensional perfectly conducting smooth targets, performed for the Electromagnetic Code Consortium. Plots are presented for both the low- and high-frequency measurements of the NASA almond, an ogive, a double ogive, a cone-sphere, and a cone-sphere with a gap.

A finite-difference, time-domain solution for three-dimensional electromagnetic modeling

Abstract: We have developed a finite-difference solution for three-dimensional (3-D) transient electromagnetic problems. The solution steps Maxwell's equations in time using a staggered-grid technique. The time-stepping uses a modified version of the Du Fort-Frankel method which is explicit and always stable. Both conductivity and magnetic permeability can be functions of space, and the model geometry can be arbitrarily complicated. The solution provides both electric and magnetic field responses throughout the earth. Because it solves the coupled, first-order Maxwell's equations, the solution avoids approximating spatial derivatives of physical properties, and thus overcomes many related numerical difficulties. Moreover, since the divergence-free condition for the magnetic field is incorporated explicitly, the solution provides accurate results for the magnetic field at late times.An inhomogeneous Dirichlet boundary condition is imposed at the surface of the earth, while a homogeneous Dirichlet condition is employed along the subsurface boundaries. Numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth-order difference method at early times and a second-order method at other times. Numerical checks against analytical, integral-equation, and spectral differential-difference solutions show that the solution provides accurate results.Execution time for a typical model is about 3.5 hours on an IBM 3090/600S computer for computing the field to 10 ms. That model contains 100 X 100 X 50 grid points representing about three million unknowns and possesses one vertical plane of symmetry, with the smallest grid spacing at 10 m and the highest resistivity at 100 Omega . m. The execution time indicates that the solution is computer intensive, but it is valuable in providing much-needed insight about TEM responses in complicated 3-D situations.

Electromagnetic induction by a finite electric dipole source over a 2-D earth

Abstract: A numerical solution for the frequency domain electromagnetic response of a two-dimensional (2-D) conductivity structure to excitation by a three-dimensional (3-D) current source has been developed. The fields are Fourier transformed in the invariant conductivity direction and then expressed in a variational form. At each of a set of discrete spatial wavenumbers a finite-element method is used to obtain a solution for the secondary electromagnetic fields. The finite element uses exponential elements to efficiently model the fields in the far-field. In combination with an iterative solution for the along-strike electromagnetic fields, this produces a considerable reduction in computation costs. The numerical solutions for a horizontal electric dipole are computed and shown to agree with closed form expressions and to converge with respect to the parameterization. Finally some simple examples of the electromagnetic fields produced by horizontal electric dipole sources at both the seafloor and air-earth interface are presented to illustrate the usefulness of the code.

Electromagnetic fields of energized conductors

Abstract: The electric field due to single-frequency current distribution in a buried horizontal rod with current leakage along its length and at its ends is computed for observation points at the soil-surface for low and high frequencies. The computation results are based on a general formulation which permits observation points in air or soil for an arbitrary network of energized conductors. The contribution of in-air and in-soil thin-wire conductors to electromagnetic fields is represented by path integrals. >

Rigorous electromagnetic modeling of chip-to-package (first-level) interconnections

Abstract: A methodology is presented for the rigorous electromagnetic analysis of pulse transmission through first-level interconnects. The methodology combines a full-wave, vectorial, time-dependent Maxwell's equations solver with SPICE circuit models for the nonlinear drivers, to facilitate the accurate modeling of the electromagnetic phenomena occurring at the chip-to-package interface. Comparisons of the results obtained using this method with others calculated using SPICE simulations are used to validate the method and demonstrate its application in the electromagnetic modeling of high-speed packaging structures. >

Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle

Abstract: Time-harmonic electromagnetic waves are scattered by a homogeneous dielectric obstacle. The corresponding electromagnetic transmission problem is reduced to a single integral equation over S for a single unknown tangential vector field, where S is the interface between the obstacle and the surrounding medium. In fact, several different integral equations are derived and analysed, including two previously-known equations due to E. Marx and J. R. Mautz, and two new singular integral equations. Mautz's equation is shown to be uniquely solvable at all frequencies. A new uniquely solvable singular integral equation is also found. The paper also includes a review of methods using pairs of coupled integral equations over S. It is these methods that are usually used in practice, although single integral equations seem to offer some computational advantages.

A fast algorithm for solving hybrid integral equation

Abstract: Based on the fast multipole method and the T-matrix formulation, an efficient approach is presented for reducing the operation count of matrix-vector multiplications in the conjugate gradient (CG) iterations to solve a hybrid (surface-volume) integral equation for a dielectric-coated metallic scatterer. The problem considered is the electromagnetic scattering of two-dimensional conductors with dielectric coating. Numerical results are given. The method given here has a computational complexity of N/sup 1.5/. It is seen that the method is more efficient than using CG directly, when the matrix filling for small N consumes a large portion of CPU time, while for the fast algorithm, there is no need to fully generate the coefficient matrix. >

Application of FDTD method to analysis of electromagnetic radiation from VLSI heatsink configurations

Abstract: The electromagnetic radiation from a VLSI chip package and heatsink structure is analyzed by means of the finite-difference-time-domain (FDTD) technique. The dimensions of a typical configuration call for a multizone gridding scheme in the FDTD algorithm to accommodate fine grid cells in the vicinity of the heatsink and package cavity and sparse gridding in the remainder of the computational domain. The issues pertaining to the effects of the heatsink on the overall radiative capacity of the configuration are addressed. Analyses are facilitated by using simplified heatsink models and by using dipole elements as sources of electromagnetic energy to model the VLSI chip. The potential for enhancement of spurious emissions by the heatsink structure is illustrated. For heatsinks of typical dimensions, resonance is possible within the low gigahertz frequency range. The exploitation of the heatsink as an emissions shield by appropriate implementation schemes is discussed and evaluated. >

Analysis of electromagnetic scattering from a cavity with a complex termination by means of a hybrid ray-FDTD method

Abstract: The electromagnetic modeling of engine cavities is a very difficult task because the electrical size of the cavity is very large, while the engine termination is geometrically complex. High-frequency techniques can adequately model the cavity, but perform poorly when applied to the termination. Low-frequency techniques are currently infeasible for such large geometries because of the large memory and computation time requirements. The authors present a hybrid method which combines the most attractive features of the lowand high-frequency techniques. The finite-difference time-domain (FDTD) method is applied to the small region surrounding the termination. The remainder of the cavity is modeled with ray methods. To validate this method, they consider two-dimensional cavities with complex terminations. Their results are compared against those found from a hybrid combination of the modal method and the method of moments. >

Circuit models for 3D structures with incident fields

Abstract: Results for a two-conductor transmission line model are compared with a new partial element equivalent model (PEEC) which has been formulated to solve the scattering problem. The PEEC model corresponds to a full-wave method-of-moments solution. Advantages of the PEEC model are numerous since it can be coupled with other circuit simulation tools. For the two-wire problem, the PEEC solution includes both the common and the differential mode currents. The transmission line model provides only the differential mode current. The new PEEC models can be solved with a conventional circuit solver like ASTAP or SPICE provided that either the retardation is very small or the solver can handle retarded sources. >

Spectral electromagnetic modeling of a planar integrated structure with a general grounded anisotropic slab

Abstract: A formulation for the solution of the electromagnetic field in vertically stratified structures with a general anisotropic grounded slab under planar electric excitation conditions is presented. The development of the solution is obtained by using the two-dimensional Fourier transform applied to the partial differential equations describing the electromagnetic field, which can be expressed in terms of dyadic electric Green's functions. Moreover, a spectral equivalent circuit representation of the solution, separated into its spectral transverse electric (TE) and transverse magnetic (TM) components (with respect to the vertical direction), is given. It is demonstrated that such a spectral circuit representation is always possible when the constitutive epsilon and mu tensors are reduced to their diagonal form. The transmission-line representation for an unbounded gyrotropic medium with vertical preferred axis is presented. This theory is applied to a planar structure with an anisotropic biaxial grounded slab and an electric horizontal point source embedded in it. Numerical examples of evaluation of the radiated pattern and noteworthy information about the radiation on the horizon plane are given. >

Modeling of power/ground plane noise in high speed digital electronics packaging

Abstract: A new model for the simulation of power/ground plane noise which is simple in principle, accurate in its solutions, and applicable to various levels of high-speed digital electronics packaging, is given. It is found that one can obtain accurate modeling of delta-I noise in power and ground planes without resorting to full-wave electromagnetic modeling. Sample results of the simulated delta-I noise with the method are shown. >

Electrodynamics of visible-light interactions with the vertebrate retinal rod.

Abstract: We report the initial investigation of the electrodynamics of visible-light interaction with the outer segment of the vertebrate retinal rod based on detailed, first-principles computational electromagnetics modeling. The computational method employs a direct time integration of Maxwell’s equations in a two-dimensional space grid for both transverse-magnetic and transverse-electric vector-field modes. Detailed maps of the optical standing wave within the retinal rod are given for three illumination wavelengths: 714, 505, and 475 nm. The standing-wave data are Fourier analyzed to obtain spatial frequency spectra. Except for isolated peaks, the spatial frequency spectra are essentially independent of the illumination wavelength.

Computation of electromagnetic fields produced by electric power lines and residential electrical wiring

Abstract: Recent epidemiological research work suggesting a link between 50-60 Hz magnetic fields and certain forms of leukemia and brain cancer has increased interest in evaluating electromagnetic fields emanating from a three-dimensional arbitrary network of energized overhead and buried conductors. Electric and magnetic fields inside and outside an imaginary house located near a power distribution line are presented. The electromagnetic fields are computed using a powerful frequency domain method. The emphasis is on modeling complex portions of residential electric circuits, buried water pipes and ground rods without necessarily duplicating an existing house or experimental equivalent. This approach is adopted deliberately. >

FDTD modeling of noise in computer packages

Abstract: The electromagnetic modeling of the components of a computer package that contribute to noise on the signal lines in computer packages is discussed. Equivalent circuits of coupled transmission lines, discontinuities in transmission lines, and a parallel-plate power plane configuration are obtained. These equivalent circuits allow one to use a circuit simulator to model the crosstalk, reflection, and simultaneous switching noises that are common in computer packages. The finite difference time domain (FDTD) algorithm is used to obtain the full-wave electromagnetic field solutions from which the equivalent circuits are determined. >

Direct Time Integration of Maxwell's Equations in 2-D Dielectric Waveguides for Propagation and Scattering of Femtosecond Electromagnetic Solitons

Abstract: Experimentalists have produced all-optical switches capable of 100-fs responses [1]. To adequately model such switches, nonlinear effects in optical materials [2] (both instantaneous and dispersive) must be included. In principle, the behavior of electromagnetic fields in nonlinear dielectrics can be determined by solving Maxwell's equations subject to the assumption that the electric polarization has a nonlinear relation to the electric field. However, until our previous work [3, 4], the resulting nonlinear Maxwell's equations have not been solved directly. Rather, approximations have been made that result in a class of generalized nonlinear Schrodinger equations (GNLSE) [5] that solve only for the envelope of the optical pulses.

Phase Error Control for FD-TD Methods

Abstract: Researchers in computational electromagnetics have recently become aware of an important property1 of finite element methods for elliptic boundary-value problems relevant to the frequency-domain Maxwell’s equations. This property relates the number of points per wavelength, N ppwto frequency, ω, through a non-linear relationship. The theoretical results are for a fixed physical domain size and relate a scaled time-frequency, k = ω/c, to the quantity kΔ = 2π/N ppw, where c is the speed of light in vacuum and Δ is the characteristic spatial scale of the discretization. Herein, we derive a property of the phase error for finite difference approximations to the time-domain Maxwell’s equations that is appropriately conjugate to that for the conjugate, frequency-domain, problem1.

Phased array antenna analysis using hybrid finite element methods

Abstract: : This research in computational electromagnetics developed a new method for predicting the near-field mutual coupling effects in phased array antennas, using the finite element method (FEM) in combination with integral equations. Accurate feed modeling is accomplished by enforcing continuity between the FEM solution and an arbitrary number of wave guide models across a ground plane aperture. A periodic integral equation is imposed above the antenna's physical structure in order to enforce the radiation condition and to confine the analysis to an array unit cell. The electric field is expanded in terms of vector finite elements, and Galerkin's method is used to write the problem as a matrix equation. A general-purpose computer code was developed and validated by comparing its results to published data for several array types. Its versatility was demonstrated with predictions of the scanning properties of arrays of printed dipoles and printed flared notches.

Modelling of electromagnetic interferences produced by a railgun

Abstract: The electromagnetic fields radiated by a railgun during its operation are evaluated at different points around the launcher. The radiation is determined, assuming a temporal and spatial form of the current in the plasma arc, and integrating the Maxwell equations directly in the time domain. In general the evaluation of the electromagnetic field expressions requires a numerical integration, while when it is possible to assume particular spatial and temporal form of the arc current, analytical expressions are derived. The results show that unacceptable electromagnetic disturbances can be produced during the arc ignition of a railgun. >

Analysis of wave propagation effects on microwave field-effect transistors

Abstract: The effects of electromagnetic wave propagation on FET electrodes are investigated by analyzing two devices: the conventional MESFET and the INGFET (inverted-gate FET) which is designed to exploit the wave propagation effects. The wave effects are analyzed using a CAD (computer-aided design) model which accounts for the semiconductor characteristics and the nonstationary electron dynamics, the electromagnetic characteristics, and the parasitic elements of the device. The importance of including the wave propagation effects in the device analysis is clearly shown in the results. It is shown that the amplification factor of the gainful mode of the INGFET is larger than that of the MESFET for higher frequencies and wider devices. Also, the INGFET exhibits higher gain when operated in the TWT mode and when terminated with 50- Omega loads. >

Spatial interpolation of the moment matrix in electromagnetic scattering and radiation problems

Abstract: In the analysis of antennas and scatterers of arbitrary shape by the method of moments (MoM), it is desirable to fill the matrix efficiently so that larger size problems can be solved. The authors describe an efficient MoM technique in which the matrix is filled by spatial interpolation of the matrix elements. Redundant calculations in the moment matrix are eliminated by utilizing various symmetries. The method is illustrated by application to planar problems including scattering from a square plate and radiation from a microstrip patch antenna. Computed results compare very well with those in the published literature. Using interpolation to fill the moment matrix has proven to be very efficient and produces negligible error in the computed current distribution. >