skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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,more » 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 element types. Thus, in addition to reducing the computational burden associated with large periodic structures, GIFFT now permits modeling these structures with source and defect elements. Relaxing the restriction to strictly identical periodic elements is, of course, useful for practical applications where, for example, a dipole excitation may be of interest or, as is often the case for metamaterials, defective elements are introduced in the structure's fabrication process. The main extensions of the GIFFT method compared to [1] are the following: (1) Both periodic ''background'' and ''source'' or ''defect'' elements are now separately defined in translatable unit cells so that, in the algorithm, mutual electromagnetic interactions can be computed. (2) The near-interaction block matrix must allow for the possibility of ''background-to-source'' or ''background-to-defect'' cell interactions. (3) Matrices representing projections of both ''background and source'' or ''background and defect'' subdomain bases onto the interpolation polynomials must be defined and appropriately selected in forming the matrix-vector product. It is important to note that, although here we consider a metamaterial layer with a dipole-antenna excitation, as per the extended GIFFT algorithm, ''defect'' elements could be considered as well.« less

Authors:
; ; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
894343
Report Number(s):
UCRL-CONF-218954
TRN: US0700151
DOE Contract Number:
W-7405-ENG-48
Resource Type:
Conference
Resource Relation:
Conference: Presented at: IEEE AP-S International Symposium, Albuquerque, NM, United States, Jul 09 - Jul 14, 2006
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGORITHMS; COMPUTERS; DEFECTS; DIPOLES; ELECTROMAGNETIC INTERACTIONS; EXCITATION; EXPLOSIONS; FABRICATION; INTERPOLATION; MATRICES; MODIFICATIONS; NUMERICAL ANALYSIS; POLYNOMIALS; SIMULATION; STORAGE

Citation Formats

Capolino, F, Basilio, L, Fasenfest, B J, and Wilton, D R. GIFFT: A Fast Solver for Modeling Sources in a Metamaterial Environment of Finite Size. United States: N. p., 2006. Web.
Capolino, F, Basilio, L, Fasenfest, B J, & Wilton, D R. GIFFT: A Fast Solver for Modeling Sources in a Metamaterial Environment of Finite Size. United States.
Capolino, F, Basilio, L, Fasenfest, B J, and Wilton, D R. Mon . "GIFFT: A Fast Solver for Modeling Sources in a Metamaterial Environment of Finite Size". United States. doi:. https://www.osti.gov/servlets/purl/894343.
@article{osti_894343,
title = {GIFFT: A Fast Solver for Modeling Sources in a Metamaterial Environment of Finite Size},
author = {Capolino, F and Basilio, L and Fasenfest, B J and Wilton, D R},
abstractNote = {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 element types. Thus, in addition to reducing the computational burden associated with large periodic structures, GIFFT now permits modeling these structures with source and defect elements. Relaxing the restriction to strictly identical periodic elements is, of course, useful for practical applications where, for example, a dipole excitation may be of interest or, as is often the case for metamaterials, defective elements are introduced in the structure's fabrication process. The main extensions of the GIFFT method compared to [1] are the following: (1) Both periodic ''background'' and ''source'' or ''defect'' elements are now separately defined in translatable unit cells so that, in the algorithm, mutual electromagnetic interactions can be computed. (2) The near-interaction block matrix must allow for the possibility of ''background-to-source'' or ''background-to-defect'' cell interactions. (3) Matrices representing projections of both ''background and source'' or ''background and defect'' subdomain bases onto the interpolation polynomials must be defined and appropriately selected in forming the matrix-vector product. It is important to note that, although here we consider a metamaterial layer with a dipole-antenna excitation, as per the extended GIFFT algorithm, ''defect'' elements could be considered as well.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jan 23 00:00:00 EST 2006},
month = {Mon Jan 23 00:00:00 EST 2006}
}

Conference:
Other availability
Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that hold this conference proceeding.

Save / Share:
  • No abstract prepared.
  • The usefulness of finite element modeling follows from the ability to accurately simulate the geometry and three-dimensional fields on the scale of a fraction of a wavelength. To make this modeling practical for engineering design, it is necessary to integrate the stages of geometry modeling and mesh generation, numerical solution of the fields-a stage heavily dependent on the efficient use of a sparse matrix equation solver, and display of field information. The stages of geometry modeling, mesh generation, and field display are commonly completed using commercially available software packages. Algorithms for the numerical solution of the fields need to bemore » written for the specific class of problems considered. Interior problems, i.e. simulating fields in waveguides and cavities, have been successfully solved using finite element methods. Exterior problems, i.e. simulating fields scattered or radiated from structures, are more difficult to model because of the need to numerically truncate the finite element mesh. To practically compute a solution to exterior problems, the domain must be truncated at some finite surface where the Sommerfeld radiation condition is enforced, either approximately or exactly. Approximate methods attempt to truncate the mesh using only local field information at each grid point, whereas exact methods are global, needing information from the entire mesh boundary. In this work, a method that couples three-dimensional finite element (FE) solutions interior to the bounding surface, with an efficient integral equation (IE) solution that exactly enforces the Sommerfeld radiation condition is developed. The bounding surface is taken to be a surface of revolution (SOR) to greatly reduce computational expense in the IE portion of the modeling.« less
  • In most photochemical grid models, the majority of the CPU time is spent numerically integrating the time evolution of (solving) the chemistry. One approach to speeding up the chemistry calculations is to use parallel computers combined with a solver developed to exploit the parallel architecture. A potential drawback to this approach is that the resulting code may be tailored to a specific computer architecture and only run efficiently on a limited number of rather expensive computing platforms. Development of a fundamentally more efficient chemistry solver is an attractive alternative since the benefits will be realized on all computing platforms. Themore » authors developed a highly efficient chemistry solver. Several numerical algorithms are built into the chemistry solver and during model runs an appropriate algorithm is selected for each {open_quotes}call{close_quotes} to the chemistry based on the chemical conditions for that call. The result is that a very fast algorithm is used most of the time but a slower, more robust algorithm is used in situations where the fast algorithm might become inaccurate. This solver has been implemented in the Urban Airshed Model (UAM), the model used for regulatory ozone modeling in the U.S. The adaptive-hybrid solver results in about a ten-fold speedup in the chemistry calculations and therefore an overall speedup in the model of 3 to 4 times. Model performance is very similar to the standard version of UAM. Most importantly, the response of ozone concentrations to changes in VOC and NO{sub x} emissions is almost identical between {open_quotes}standard{close_quotes} and {open_quotes}fast{close_quotes} versions of UAM. Use of the fast solver does not change any conclusions that would be drawn about model performance relative to observations or the effectiveness of emission control strategies. This paper will describe the methodology used in our adaptive-hybrid fast chemistry solver and present results of its implementation in UAM.« less
  • No abstract prepared.
  • Abstract not provided.