15 Matching Results

Search Results

Advanced search parameters have been applied.

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

Numerical Modeling of Left-Handed Metamaterials

Description: The EIGER method of moments program with periodic Green's function was used to model a periodic array of strips and split-ring resonators. Left-handed propagation due to negative index of refraction is demonstrated in a frequency band. The effective material parameters versus frequency are extracted from the EIGER solution.
Date: November 6, 2001
Creator: Burke, G J; Champagne, N J & Sharpe, R M
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

Mixed Electromagnetic and Circuit Simulations using Higher-Order Elements and Bases

Description: In this paper, an approach to couple higher-order electromagnetic surface integral equations to circuit simulations is presented. Terminals are defined that connect circuit elements to contacts modeled on the distributed electromagnetic domain. A modified charge-current continuity equation is proposed for a generalized KCL connection at the contacts. The distributive electromagnetic integral equations are developed using higher-order bases and elements that allow both better convergence and accuracy for modeling. The resulting scheme enables simultaneous solution of electromagnetic integral equations for arbitrarily-shaped objects and SPICE-like modeling for lumped circuits, and permits design iterations and visualization of the interaction between the two domains.
Date: June 18, 2003
Creator: Champagne, N J; Rockway, J D & Jandhyala, V
Partner: UNT Libraries Government Documents Department

EIGER: Electromagnetic Interactions GEneRalized

Description: The EIGER (Electromagnetic Interactions Generalized) modeling suite is a joint development activity by the Lawrence Livermore National Lab, Sandia National Labs, the University of Houston, and the Navy (Space and Naval Warfare Systems Center-San Diego). The effort endeavors to bring the next generation of hybrid, higher-order, full-wave analysis methods into a single integrated framework. The tools are based upon frequency-domain solutions of Maxwell's equations to model scattering and radiation from complex 2D and 3D structures. The framework employs boundary element solutions of integral equation formulations and finite element solutions of the Helmholtz wave equation. A goal is to use higher-order representations to model both the geometry (using higher-order geometric elements) and numerical methods (using higher-order vector basis functions). In addition, a variety of advanced Green's functions and symmetry operators can be applied to efficiently treat geometries containing such features as layered material regions and periodic structures. Each of these methods can be brought to bear simultaneously, on different portions of a complex structure. HPC implementation issues were addressed during the design of the software architecture, so that the same package runs on platforms ranging from serial desktop workstations through advanced HPC architectures. Our current efforts on higher-order modeling and improved solver libraries will be highlighted.
Date: June 13, 2001
Creator: Champagne, N J; Sharpe, R M & Rockway, J W
Partner: UNT Libraries Government Documents Department

Fresnel Integral Equations: Numerical Properties

Description: A spatial-domain solution to the problem of electromagnetic scattering from a dielectric half-space is outlined. The resulting half-space operators are referred to as Fresnel surface integral operators. When used as preconditioners for nonplanar geometries, the Fresnel operators yield surface Fresnel integral equations (FIEs) which are stable with respect to dielectric constant, discretization, and frequency. Numerical properties of the formulations are discussed.
Date: July 22, 2003
Creator: Adams, R J; Champagne, N J II & Davis, B A
Partner: UNT Libraries Government Documents Department

Mixed Electromagnetic and Circuit Simulations using a Higher-Order Hybrid Formulation

Description: Standard surface impedance approximations are invalid at lower frequencies approaching DC since the cross sections of conductors are smaller than the skin depth. Hence, a volumetric formulation is typically used at these low frequencies for broadband simulation as necessitated in digital or ultra-wideband systems since the skin effect can be modeled explicitly. This modeling requires fine and frequency dependent volume meshing. However, an approach using higher-order elements and/or bases may alleviate these requirements. The intent of this paper is to present a tightly coupled circuit and hybrid boundary element (or integral equation)/finite element based electromagnetic simulation that has been coded in EIGER.
Date: January 14, 2004
Creator: Champagne, N J; Jandhyala, V & Rockway, J D
Partner: UNT Libraries Government Documents Department

A Generalized Fast Frequency Sweep Algorithm for Coupled Circuit-EM Simulations

Description: Frequency domain techniques are popular for analyzing electromagnetics (EM) and coupled circuit-EM problems. These techniques, such as the method of moments (MoM) and the finite element method (FEM), are used to determine the response of the EM portion of the problem at a single frequency. Since only one frequency is solved at a time, it may take a long time to calculate the parameters for wideband devices. In this paper, a fast frequency sweep based on the Asymptotic Wave Expansion (AWE) method is developed and applied to generalized mixed circuit-EM problems. The AWE method, which was originally developed for lumped-load circuit simulations, has recently been shown to be effective at quasi-static and low frequency full-wave simulations. Here it is applied to a full-wave MoM solver, capable of solving for metals, dielectrics, and coupled circuit-EM problems.
Date: January 14, 2004
Creator: Rockway, J D; Champagne, N J; Sharpe, R M & Fasenfest, B
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

Differential Forms Basis Functions for Better Conditioned Integral Equations

Description: Differential forms offer a convenient way to classify physical quantities and set up computational problems. By observing the dimensionality and type of derivatives (divergence,curl,gradient) applied to a quantity, an appropriate differential form can be chosen for that quantity. To use these differential forms in a simulation, the forms must be discretized using basis functions. The 0-form through 2-form basis functions are formed for surfaces. Twisted 1-form and 2-form bases will be presented in this paper. Twisted 1-form (1-forms) basis functions ({Lambda}) are divergence-conforming edge basis functions with units m{sup -1}. They are appropriate for representing vector quantities with continuous normal components, and they belong to the same function space as the commonly used RWG bases [1]. They are used here to formulate the frequency-domain EFIE with Galerkin testing. The 2-form basis functions (f) are scalar basis functions with units m{sup -2} and with no enforced continuity between elements. At lowest order, the 2-form basis functions are similar to pulse basis functions. They are used here to formulate an electrostatic integral equation. It should be noted that the derivative of an n-form differential form basis function is an (n+1)-form, i.e. the derivative of a 1-form basis function is a 2-form. Because the basis functions are constructed such that they have spatial units, the spatial units are removed from the degrees of freedom, leading to a better-conditioned system matrix. In this conference paper, we look at the performance of these differential forms and bases by examining the conditioning of matrix systems for electrostatics and the EFIE. The meshes used were refined across the object to consider the behavior of these basis transforms for elements of different sizes.
Date: January 13, 2005
Creator: Fasenfest, B; White, D; Stowell, M; Rieben, R; Sharpe, R; Madsen, N et al.
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