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GIFFT: A Fast Solver for Modeling Sources in a Metamaterial Environment of Finite Size

Description: Due to the recent explosion of interest in studying the electromagnetic behavior of large (truncated) periodic structures such as phased arrays, frequency-selective surfaces, and metamaterials, there has been a renewed interest in efficiently modeling such structures. Since straightforward numerical analyses of large, finite structures (i.e., explicitly meshing and computing interactions between all mesh elements of the entire structure) involve significant memory storage and computation times, much effort is currently being expended on developing techniques that minimize the high demand on computer resources. One such technique that belongs to the class of fast solvers for large periodic structures is the GIFFT algorithm (Green's function interpolation and FFT), which is first discussed in [1]. This method is a modification of the adaptive integral method (AIM) [2], a technique based on the projection of subdomain basis functions onto a rectangular grid. Like the methods presented in [3]-[4], the GIFFT algorithm is an extension of the AIM method in that it uses basis-function projections onto a rectangular grid through Lagrange interpolating polynomials. The use of a rectangular grid results in a matrix-vector product that is convolutional in form and can thus be evaluated using FFTs. Although our method differs from [3]-[6] in various respects, the primary differences between the AIM approach [2] and the GIFFT method [1] is the latter's use of interpolation to represent the Green's function (GF) and its specialization to periodic structures by taking into account the reusability properties of matrices that arise from interactions between identical cell elements. The present work extends the GIFFT algorithm to allow for a complete numerical analysis of a periodic structure excited by dipole source, as shown in Fig 1. Although GIFFT [1] was originally developed to handle strictly periodic structures, the technique has now been extended to efficiently handle a small number of distinct ...
Date: January 23, 2006
Creator: Capolino, F; Basilio, L; Fasenfest, B J & Wilton, D R
Partner: UNT Libraries Government Documents Department

The Analysis of Thin Wires Using Higher-Order Elements and Basis Functions

Description: Thin wire analysis was applied to curved wire segments in [1], but a special procedure was needed to evaluate the self and near-self terms. The procedure involved associating the singular behavior with a straight segment tangent to the curved source segment, permitting use of algorithms for straight wires. Recently, a procedure that avoids the singularity extraction for straight wires was presented in [2-4]. In this paper, the approach in [4] is applied to curved (or higher-order) wires using a procedure similar to that used in [1] for singularity extraction. Here, the straight tangent segment is used to determine the quadrature rules to be used on the curved segment. The result is a formulation that allows for a general mixture of higher-order basis functions [5] and higher-order wire segments.
Date: January 23, 2006
Creator: Champagne, N. J.; Wilton, D. R. & Rockway, J. W.
Partner: UNT Libraries Government Documents Department

Efficient computation of periodic and nonperiodic Green`s functions in layered media using the MPIE

Description: The mixed potential integral equation (MPIE) formulation is convenient for problems involving layered media because potential quantities involve low order singularities, in comparison to field quantities. For nonperiodic problems, the associated Green`s potentials involve spectral integrals of the Sommerfeld type, in the periodic case, discrete sums over sampled values of the same spectra are required. When source and observation points are in the same or in adjacent layers, the convergence of both representations is enhanced by isolating the direct and quasi-static image contributions associated with the nearby layers. In the periodic case, the convergence of direct and image contributions may be rapidly accelerated by means of the Ewadd method.
Date: March 27, 1998
Creator: Wilton, D.R.; Jackson, D.R. & Champagne, N.J.
Partner: UNT Libraries Government Documents Department

On Attaching a Wire to a Triangulated Surface

Description: There have been many papers that have focused on the attachment of wires to surfaces. The focus of this paper will be on wires connected to arbitrarily shaped surfaces, a body that may be modeled with triangles as described in [1]. The basis function for the wire-to-surface junction is constructed by building the 1/r variation of the surface current near the junction into the surface current. In the following we summarize junction bases as currently used. In the presentation we consider their numerical implementation, examine alternative formulations, and review validation studies that prove the approach is robust with respect to wire orientation and surface geometry at the junction.
Date: January 28, 2002
Creator: Champagne, N J; Johnson, W A & Wilton, D R
Partner: UNT Libraries Government Documents Department

General MoM Solutions for Large Arrays

Description: This paper focuses on a numerical procedure that addresses the difficulties of dealing with large, finite arrays while preserving the generality and robustness of full-wave methods. We present a fast method based on approximating interactions between sufficiently separated array elements via a relatively coarse interpolation of the Green's function on a uniform grid commensurate with the array's periodicity. The interaction between the basis and testing functions is reduced to a three-stage process. The first stage is a projection of standard (e.g., RWG) subdomain bases onto a set of interpolation functions that interpolate the Green's function on the array face. This projection, which is used in a matrix/vector product for each array cell in an iterative solution process, need only be carried out once for a single cell and results in a low-rank matrix. An intermediate stage matrix/vector product computation involving the uniformly sampled Green's function is of convolutional form in the lateral (transverse) directions so that a 2D FFT may be used. The final stage is a third matrix/vector product computation involving a matrix resulting from projecting testing functions onto the Green's function interpolation functions; the low-rank matrix is either identical to (using Galerkin's method) or similar to that for the bases projection. An effective MoM solution scheme is developed for large arrays using a modification of the AIM (Adaptive Integral Method) method. The method permits the analysis of arrays with arbitrary contours and nonplanar elements. Both fill and solve times within the MoM method are improved with respect to more standard MoM solvers.
Date: July 22, 2003
Creator: Fasenfest, B; Capolino, F; Wilton, D R; Jackson, D R & Champagne, N
Partner: UNT Libraries Government Documents Department

EIGER: A new generation of computational electromagnetics tools

Description: The EIGER project (Electromagnetic Interactions GenERalized) endeavors to bring the next generation of spectral domain electromagnetic analysis tools to maturity and to cast them in a general form which is amenable to a variety of applications. The tools are written in Fortran 90 and with an object oriented philosophy to yield a package that is easily ported to a variety of platforms, simply maintained, and above all efficiently modified to address wide ranging applications. The modular development style and the choice of Fortran 90 is also driven by the desire to run efficiently on existing high performance computer platforms and to remain flexible for new architectures that are anticipated. The electromagnetic tool box consists of extremely accurate physics models for 2D and 3D electromagnetic scattering, radiation, and penetration problems. The models include surface and volume formulations for conductors and complex materials. In addition, realistic excitations and symmetries are incorporated, as well as, complex environments through the use of Green`s functions.
Date: March 1996
Creator: Wilton, D. R.; Johnson, W. A.; Jorgenson, R. E.; Sharpe, R. M. & Grant, J. B.
Partner: UNT Libraries Government Documents Department

Electromagnetic Interactions GEneRalized (EIGER): Algorithm abstraction and HPC implementation

Description: Modern software development methods combined with key generalizations of standard computational algorithms enable the development of a new class of electromagnetic modeling tools. This paper describes current and anticipated capabilities of a frequency domain modeling code, EIGER, which has an extremely wide range of applicability. In addition, software implementation methods and high performance computing issues are discussed.
Date: June 1, 1998
Creator: Sharpe, R.M.; Grant, J.B.; Champagne, N.J.; Wilton, D.R.; Jackson, D.R.; Johnson, W.A. et al.
Partner: UNT Libraries Government Documents Department