Richard Holland

Finite-Difference Solution of Maxwell's Equations in Generalized Nonorthogonal Coordinates

This article describes a time-domain finite-difference algorithm for solving Maxwells equations in generalized nonorthogonal coordinates. We believe this approach would be most useful for applications where a uniform, uncurved, but oblique, meshing scheme could be applied in lieu of staircasing. This algorithm is similar to conventional leapfrog-differencing schemes, but now an additional leapfrogging between covariant and contravariant field representations becomes necessary.

Finite-Difference Analysis of EMP Coupling to Thin Struts and Wires

This paper describes the implementation of the thin-strut formalism in the 3-D EMP time-domain finite-difference code THREDE. The thin-strut formalism permits inclusion of arbitrary fine wires in THREDE without imposing any corresponding demand to reduce the cell size to the wire size. The keystone of this technique is the so-called in-cell inductance-the inductance per unit length a thin wire would have with respect to an enclosing conductor half a cell removed. THREDE results using this formalism are compared with analytic EMP solutions for a linear dipole antenna and a loop antenna. Errors are around 10 percent for the loop and 7 percent for the dipole. The 10-percent loop error could probably be improved; the 7-percent dipole error seems to be fundamental to the basic THREDE approximations.

THREDE: A Free-Field EMP Coupling and Scattering Code

THREDE is a time-domain, linear, finite-difference, three-dimensional EMP coupling and scattering code. In its present form, it can accomodate a problem space consisting of a 30×30×30 mesh. Differencing is linear. Problem-space boundaries are provided with a radiating condition which does not generate ficticious mathematical echos at late times. The scatterer must be a perfect conductor, although a nonideal ground plane (runway) may be close by. The present article describes the mathematical basis of THREDE, and shows the results of applying it to predict the response of an F-111 shell in the horizontally-polarized dipole (HPD) EMP simulator. Amplitude agreement between experiment and prediction for this example is typically on the order of 20%; resonant frequencies are predicted more closely than this. THREDE costs about 1 second of CDC 7600 computer time per program cycle; most practical analyses require 500 to 1000 program cycles.

Finite-Difference Analysis of EMP Coupling to Lossy Dielectric Structures

This article describes the 3-D EMP finite-difference time-domain computer code THREDE as generalized to calculate coupling to, and scattering from, lossy dielectric objects. The code primarily treats the scattered component of the electromagnetic fields (thus presuming linearity) and employs a radiating outer boundary. As sample scatterers, we use dielectric spheres of ¿ = 2¿0 and 9¿0 illuninated by an EMP plane wave of double exponential profile. Comparitive calculations were made using the inverse-Fourier transform of the Rayleigh-Mie spherical-hannonic expansion solution-agreement of the two solutions is very good.

Implementation of the Thin-Slot Formalism in the Finite-Difference EMP Code THREDII

This article derives the thin-slot formalism in a manner compatible with the 3D EMP time-domain finite-difference code THREDII. The thin-slot formalism permits inclusion of conducting plates with arbitrarily narrow slots or gaps without requiring any corresponding need to reduce the cell size to the gap width. The basic concept of this formalism is to increase the effective ¿ seen by the electric field across the gap and to reduce, in proportion, the ¿ seen by the magnetic field transverse to the gap. The conducting plate and gap may be imbedded in a lossy medium, and the material on the two sides of the gap may be dissimilar.

Total-Field versus Scattered-Field Finite-Difference Codes: A Comparative Assessment

This paper deals with time-domain finite-difference (TDFD) techniques for solutions of Maxwells equations. Two types of algorithms are treated: scattered-field algorithms in which the incident fields (E¿i,H¿i), are analytically known but the scattered fields (E¿s,H¿s) must be computed with TDFD methods, and total-field calculations in which total fields (E¿T,H¿T) are found by TDFD techniques. Nonlinear problems and heavily shielded cavities can only be treated with the total-field approach. The price of this generality is an increase in mathematical complexity and computational cost.

THREDS: A Finite-Difference Time-Domain EMP Code in 3d Spherical Coordinates

This article illustrates the three-dimensional time-domain finite differencing of Maxwells equations in spherical coordinates when azimuthal asymmetry is present. Problems occurring on the coordinate system axis are discussed, and the ease of implementing a radiating outer boundary in spherical coordinates is demonstrated. Sample problems show that the radiating outer boundary is usually better applied on H¿ than on E¿, and that a linearly interpolating outer boundary may be as effective as the more complicated parabolically interpolating one.

Finite-volume time-domain (FVTD) techniques for EM scattering

The authors document our efforts to compute radar cross sections using a generalization of the FDTD (finite difference time domain) Yee algorithm (1966) in which a nonorthogonal target-conforming mesh may be applied. Both 2D and 3D formulations are presented, although at present they only have 2D numerical results. Two-dimensional problems considered involve an S-shaped duct (S-duct) and an ogive. At least nine distinct resonances are correctly predicted by the S-duct model. The primary goal is to model oblique or curved surfaces without the use of staircasing. >

Contour extensional resonant properties of rectangular piezoelectric plates

This paper describes the results of an extensive theoretical study on the elastic contour extensional modes of planarly isotropic, rectangular piezoelectric plates. Results include numerical data on the resonant frequency, displacement pattern, and dynamic capacitance or dynamic coupling coefficient of the first fifty modes as a function of the length-to-width ratio. It is found that the resonances of this type of plate may be divided into four distinct and decoup1ed symmetry families. Calculated values for the resonant frequency vary in accuracy from about 0.2% for the first mode of each family to 1% for the twelfth mode. Dynamic coupling coefficient calculations are accurate to about 10%.

Statistical response of EM-driven cables inside an overmoded enclosure

This paper deals with probabilistic modeling of the electromagnetic (EM) response of cables inside a complex cavity subjected to well overmoded EM penetration. Theoretical studies indicate that the field amplitudes and cable currents squared both should have a /spl chi/-square distribution with two degrees of freedom, but our observations indicate that a log normal fit is empirically better unless the data, if experimentally obtained, is first passed through a carefully tailored trend-removing filter. If a cable model is driven by statistically simulated enclosure fields, similar extreme care must be taken with the numerical generation of these driving fields. The major innovation reported here is the development of an algorithm that models cable-drive fields simultaneously having a /spl chi/-square power-flux distribution and the physically mandated local autocorrelation at a spatial point as the frequency is swept or at a fixed frequency as the power flux sensor is moved around to map the cavity response. Nature is quite adept at creating a cable drive with these simultaneous attributes, but computer emulation had proved very exasperating. Our algorithm, as an unplanned bonus, also has the capability to transform random numbers from one distribution to another. For instance, one can input normally distributed power-flux values and obtain as the output /spl chi/-square or log normally distributed power-flux values. The reverse transformations are also allowed.