On the Implementation and Performance of Iterative Methods for Computational Electromagnetics (Scattering, Moment-Method, Conjugate-Gradient)
Peterson, Andrew Francis
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https://hdl.handle.net/2142/69335
Description
Title
On the Implementation and Performance of Iterative Methods for Computational Electromagnetics (Scattering, Moment-Method, Conjugate-Gradient)
Author(s)
Peterson, Andrew Francis
Issue Date
1986
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Abstract
The numerical solution of electromagnetic scattering problems involves approximating an exact equation by a finite-dimensional matrix equation. The use of an iterative algorithm to solve the matrix equation sometimes results in a considerable savings in computer memory requirements. For a fixed amount of computer memory, this approach permits the analysis of scatterers that are an order of magnitude larger electrically.
Iterative algorithms of the conjugate gradient class are examined and applied to a variety of typical electromagnetic scattering problems, in order to evaluate their performance in practice. In contrast with the simple iterative algorithms used in the past, which often diverged when applied to electromagnetics problems, these algorithms never diverge and usually converge at a quick rate.
Depending on the geometry of the scatterer under consideration, it may be possible to build symmetries into the matrix representation and effect the necessary storage reduction. Two distinct approaches for creating these symmetries are examined. An alternate procedure, which requires some of the matrix elements to be regenerated as needed by the iterative algorithm in use, does not rely on symmetries and is applicable to a larger set of geometries. Both procedures are applied to several scattering problems. Execution time comparisons show that the approaches based on symmetries are the most efficient, and that both procedures can be superior to noniterative techniques for large scatterers.
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