Iterative solution of the normal-equations form of the electric-field integral equation

Date
2007
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Source Title
Proceedings of the Antennas and Propagation Society International Symposium, IEEE 2007
Print ISSN
1522-3965
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Publisher
IEEE
Volume
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Pages
1857 - 1860
Language
English
Type
Conference Paper
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Abstract

In this paper, we show that transforming the original equations into normal equations improves the convergence of EFIE significantly. We present the solutions of EFIE by employing the least-squares QR (LSQR) algorithm, which corresponds to a stable application of the conjugate gradient (CG) algorithm on the normal equations. Despite the squaring of the condition number due to such a transformation into the normal equations, LSQR improves the convergence rate of the iterative solutions of EFIE and performs better than many other iterative algorithms that are commonly used in the literature. In addition to LSQR, we present the accelerated convergence of the normal equations in the context of the generalized minimal residual (GMRES) algorithm, where the memory requirement is reduced significantly due to the improved convergence characteristics.

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Keywords
Integral equations, Iterative algorithms, MLFMA, Surface waves, Computational electromagnetics, Electromagnetic scattering, Computational geometry
Citation
Published Version (Please cite this version)