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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

EIGER: Electromagnetic Interactions GEneRalized

Description: EIGER (Electromagnetic Interactions GEneRalized), a single integrated software tool set, brings together a variety of spectral domain analysis methods. These include moment method solutions of integral equation formulations and finite elements solutions of partial differential equations. New software engineering methods, specifically, object oriented design, are being used to implement abstractions of key components of spectral analysis methods so that the tools can be easily modified and extended to treat new classes of problems. The key components of the numerical analysis tool, and their roles, are: elements - to describe the geometry, basis (expansion) functions - to interpolate the unknowns (e.g., fields) locally, and operators - to express the underlying physics formulations used to propagate the energy or enforce fundamental principals. The development of EMPACK provided the fundamental impetus for these abstractions which are discussed more fully in subsequent sections. This design approach is in contrast to standard design procedures where entire codes are developed around a particular element type with a specific basis function for a single operator. Although such tools can be effectively used to model large classes of problems, it is often very difficult, if not intractable, to extend the tools beyond their initial design. Overcoming this limitation is one of the most compelling goals of this project. We have successfully overcome roadblocks encountered in extension of past development efforts, such as the extension of Patch to treat wires and wire-surface junctions in the presence of non-homogeneous media. Moreover, the application base for EIGER grows as we cast a variety of Green`s functions into a form compatible with the numerical procedures in EIGER.
Date: March 1, 1997
Creator: Sharpe, R. M.; Grant, J. B. & Champagne, N. J.
Partner: UNT Libraries Government Documents Department

An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition

Description: An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach.
Date: February 28, 2007
Creator: Madsen, N; Fasenfest, B J; White, D; Stowell, M; Jandhyala, V; Pingenot, J et al.
Partner: UNT Libraries Government Documents Department

A hybrid FEM-BEM unified boundary condition with sub-cycling for electromagnetic radiation

Description: Hybrid solutions to time-domain electromagnetic problems offer many advantages when solving open-region scattering or radiation problems. Hybrid formulations use a finite-element or finite-difference discretization for the features of interest, then bound this region with a layer of planar boundary elements. The use of volume discretization allows for intricate features and many changes in material within the structure, while the boundary-elements provide a highly accurate radiating boundary condition. This concept has been implemented previously, using the boundary elements to set the E-field, H-field, or both for an FDTD grid, for example in [1][2][3], or as a mixed boundary condition for the second order wave equation solved by finite elements [4]. Further study has focused on using fast methods, such as the Plane Wave Time Domain method [3][4] to accelerate the BEM calculations. This paper details a hybrid solver using the coupled first-order equations for the E and H fields in the finite-element region. This formulation is explicit, with a restriction on the time step for stability. When this time step is used in conjunction with the boundary elements forming either a inhomogeneous Dirichlet or Neuman boundary condition on the finite-element mesh, late time instabilities occur. To combat this, a Unified Boundary Condition (UBC), similar to the one in [4] for the second-order wave equation, is used. Even when this UBC is used, the late time instabilities are merely delayed if standard testing in time is used. However, the late time instabilities can be removed by replacing centroid based time interpolation with quadrature point based time interpolation for the boundary elements, or by sub-cycling the boundary element portion of the formulation. This sub-cycling, used in [3] for FDTD to reduce complexity, is shown here to improve stability and overall accuracy of the technique.
Date: January 12, 2006
Creator: Fasenfest, B; White, D; Stowell, M; Rieben, R; Sharpe, R; Madsen, N et al.
Partner: UNT Libraries Government Documents Department

A finite-difference frequency-domain code for electromagnetic induction tomography

Description: We are developing a new 3D code for application to electromagnetic induction tomography and applications to environmental imaging problems. We have used the finite-difference frequency- domain formulation of Beilenhoff et al. (1992) and the anisotropic PML (perfectly matched layer) approach (Berenger, 1994) to specify boundary conditions following Wu et al. (1997). PML deals with the fact that the computations must be done in a finite domain even though the real problem is effectively of infinite extent. The resulting formulas for the forward solver reduce to a problem of the form Ax = y, where A is a non-Hermitian matrix with real values off the diagonal and complex values along its diagonal. The matrix A may be either symmetric or nonsymmetric depending on details of the boundary conditions chosen (i.e., the particular PML used in the application). The basic equation must be solved for the vector x (which represents field quantities such as electric and magnetic fields) with the vector y determined by the boundary conditions and transmitter location. Of the many forward solvers that could be used for this system, relatively few have been thoroughly tested for the type of matrix encountered in our problem. Our studies of the stability characteristics of the Bi-CG algorithm raised questions about its reliability and uniform accuracy for this application. We have found the stability characteristics of Bi-CGSTAB [an alternative developed by van der Vorst (1992) for such problems] to be entirely adequate for our application, whereas the standard Bi-CG was quite inadequate. We have also done extensive validation of our code using semianalytical results as well as other codes. The new code is written in Fortran and is designed to be easily parallelized, but we have not yet tested this feature of the code. An adjoint method is being developed for solving the ...
Date: December 17, 1998
Creator: Sharpe, R M; Berryman, J G; Buettner, H M; Champagne, N J.,II & 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