Robert J. Burkholder

The generalized forward-backward method for analyzing the scattering from targets on ocean-like rough surfaces

The iterative forward backward (FB) method has been proposed to solve the magnetic field integral equation for smooth one-dimensional rough surfaces. This method has proved to be very efficient, converging in a very small number of iterations. Nevertheless, this solution becomes unstable when some obstacle, like a ship or a large breaking wave, is included in the original problem. In this paper we propose a new extension of the FB method: the generalized forward backward (GFB) method, to solve such kinds of composite problems.

Loop star basis functions and a robust preconditioner for EFIE scattering problems

An electric field integral equation (EFIE) formulation using the loop-star basis functions has been developed for modeling plane wave scattering from perfect conducting objects. A stability analysis at the DC limit shows that the use of the Rao-Wilton-Glisson (RWG) basis functions results in a singular matrix operator. However, the use of the loop-star basis functions results in a well-conditioned matrix. Moreover, a preconditioner constructed from a two-step process, based on near interactions and an incomplete factorization with a heuristic drop strategy, has been proposed in conjunction with the conjugate gradient method to solve the resulting matrix equation. The approach is shown to be effective for resolving both the low frequency instability and the bad conditioning of the EFIE method. The computational complexity of the proposed approach is shown to be O(N/sup 2/).

Modal, ray, and beam techniques for analyzing the EM scattering by open-ended waveguide cavities

The problem of high-frequency electromagnetic scattering by open-ended waveguide cavities with an interior termination is analyzed via three different approaches. When cavities can be adequately modeled by joining together piecewise separable waveguide sections, a hybrid combination of asymptotic high-frequency and modal techniques is employed. In the case of more arbitrarily shaped waveguide cavities for which modes cannot even be defined in the conventional sense, the geometrical optics ray approach proves to be highly useful. However, at sufficiently high frequencies, both of these approaches tend to become inefficient; hence, a paraxial Gaussian beam technique, which retains much of the simplicity of the ray approximation but is potentially more efficient, is investigated. Typical numerical results based on the different approaches are discussed. >

Novel Gaussian beam method for the rapid analysis of large reflector antennas

A relatively fast and simple method utilizing Gaussian beams (GBs) is developed which requires only a few seconds on a workstation to compute the near/far fields of electrically large reflector antennas when they are illuminated by a feed with a known radiation pattern. This GB technique is fast, because it completely avoids any numerical integration on the large reflector surface which is required in the conventional physical optics (PO) analysis of such antennas and which could take several hours on a workstation. Specifically, the known feed radiation field is represented by a set of relatively few, rotationally symmetric GBs that are launched radially out from the feed plane and with almost identical interbeam angular spacing. These GBs strike the reflector surface from where they are reflected, and also diffracted by the reflector edge; the expressions for the fields reflected and diffracted by the reflector illuminated with a general astigmatic incident GB from an arbitrary direction (but not close to grazing on the reflector) have been developed in Chou and Pathak (1997) and utilized in this work. Numerical results are presented to illustrate the versatility, accuracy, and efficiency of this GB method when it is used for analyzing general offset parabolic reflectors with a single feed or an array feed, as well as for analyzing nonparabolic reflectors such as those described by ellipsoidal and even general shaped surfaces.

Efficient method of moments formulation for large PEC scattering problems using asymptotic phasefront extraction (APE)

A method is introduced for reducing the exorbitant dependence on computer storage and solution time in the method of moments (MoM) for electrically large electromagnetic (EM) scattering problems. The unknown surface currents on large, smooth parts of a perfect electrical conductor (PEC) scatterer are expressed by an efficient set of linearly phased surface current basis functions. The phasefront characteristics of the surface currents are numerically extracted from known current samples obtained from a lower-frequency solution of the same configuration. The use of such basis functions for efficiently representing the surface currents that are constructed in terms of linearly phased currents at higher frequencies is justified by considering the form of the surface currents predicted by high-frequency asymptotic ray methods. The procedure for extracting the current phasefronts is purely numerical, obviating computationally expensive and nonrobust operations such as ray-tracing, and thus, is amenable to general purpose scattering codes. The new MoM with linearly phased basis functions is shown to greatly relieve the storage and solution time of the conventional MoM while accurately reproducing the induced surface currents and scattered fields of some chosen targets.

Forward-backward iterative physical optics algorithm for computing the RCS of open-ended cavities

The forward-backward methodology is combined with the iterative physical optics (IPO) algorithm to improve convergence for cavity scattering problems. Wave propagation inside elongated cavities, such as jet engine inlet ducts, follows a predominant down-and-back path. The forward-backward method allows the IPO currents on the cavity walls to be updated sequentially (forward) and reverse-sequentially (backward) along the waveguide axis. A relaxation parameter is introduced to help control the convergence characteristics, making the new algorithm mathematically equivalent to the classical iterative method of symmetric successive over-relaxation. The fast far-field approximation (FaFFA) accelerates the matrix-vector products in the IPO formulation, and an equivalent surface impedance is used to characterize thin material linings in the cavity.

Coupled canonical grid/discrete dipole approach for computing scattering from objects above or below a rough interface

A numerical model for computing scattering from a three-dimensional (3D) dielectric object above or below a rough interface is described. The model is based on an iterative method of moments solution for equivalent electric and magnetic surface current densities on the rough interface and equivalent volumetric electric currents in the penetrable object. To improve computational efficiency, the canonical grid method and the discrete dipole approach (DDA) are used to compute surface to surface and object to object point couplings, respectively, in O(N log N), where N is the number of surface or object sampling points. Two distinct iterative approaches and a preconditioning method for the resulting matrix equation are discussed, and the solution is verified through comparison with a Sommerfeld integral-based solution in the flat surface limit. Results are illustrated for a sample landmine detection problem and show that a slight surface roughness can modify object backscattering returns.

The application of FDTD in hybrid methods for cavity scattering analysis

In a previous paper (see ibid., vol.41, p.1560-1569, no.11, 1993), we presented the hybrid ray-FDTD method for analyzing the electromagnetic scattering from two-dimensional cavities with complex terminations. In this paper, we present three hybrid methods for analyzing the scattering from three-dimensional (3-D) inlet cavities. In these hybrid methods, the finite-difference time-domain (FDTD) method is used to determine the reflection matrix associated with the termination. Modal analysis, physical optics (PO), or rays are used to analyze the remaining front section of the cavity. Representative results are presented. >

A Numerical Study of the Retrieval of Sea Surface Height Profiles From Low Grazing Angle Radar Data

A numerical study of the retrieval of sea surface height profiles from low grazing angle radar observations is described. The study is based on a numerical method for electromagnetic scattering from 1-D rough sea profiles, combined with the ldquoimproved linear representationrdquo of Creamer for simulating weakly nonlinear sea surface hydrodynamics. Numerical computations are performed for frequencies from 2975 to 3025 MHz so that simulated radar pulse returns are achieved. The geometry utilized models a radar with an antenna height of 14 m, observing the sea surface at ranges from 520 to 1720 m. The low grazing angles of this configuration produce significant shadowing of the sea surface, and standard analytical theories of sea scattering are not directly applicable. Three approaches for retrieving sea height profile information are compared. The first method uses a statistical relationship between the surface height and the computed radar cross sections versus range (an incoherent measurement). A second method uses the phase difference between scattering measurements in two vertically separated antennas (ldquovertical interferometry) in the retrieval. The final technique retrieves height profiles from variations in the apparent Doppler frequency (coherent measurements) versus range and requires that time-stepped simulations be performed. The relative advantages and disadvantages of each of the three approaches are examined and discussed.

High‐frequency electromagnetic scattering by open‐ended waveguide cavities

Some approaches for analyzing the high-frequency electromagnetic scattering by open-ended waveguide cavities with a planar interior termination are discussed. The contribution to scattering arising from the open end is found using the geometrical theory of diffraction based equivalent current method, while the interior cavity scattering contribution can be treated by several different approaches, for example, hybrid modal, ray, or beam methods; other contributions are ignored for the reasons outlined in the paper. Numerical results based on these methods are presented.