Error and convergence in numerical implementations of the conjugate gradient method (EM problems)

1 December 1988

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation

Vol. 36 (12) , 1824-1827
https://doi.org/10.1109/8.14405

Abstract

The conjugate gradient method has previously been applied in electromagnetics in two ways: to moment method matrices and directly to continuous operator equations. Numerical implementations of these two methods are shown here to be equivalent. It is concluded that the advantage of the conjugate gradient method is therefore its potential computational efficiency as a solution procedure, not its ability to achieve a more exact solution than the moment method.

Keywords

This publication has 12 references indexed in Scilit:

Some of the misconceptions associated with the conjugate gradient method
Published by Institute of Electrical and Electronics Engineers (IEEE) ,2005
Resonance frequency of a rectangular microstrip patch
IEEE Transactions on Antennas and Propagation, 1988
Comments on "Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies"
IEEE Transactions on Antennas and Propagation, 1987
The conjugate gradient method as applied to electromagnetic field problems
IEEE Antennas and Propagation Society Newsletter, 1986
Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies
IEEE Transactions on Antennas and Propagation, 1986
AN ANALYSIS OF THE SPECTRAL ITERATIVE TECHNIQUE FOR ELECTROMAGNETIC SCATTERING FROM INDIVIDUAL AND PERIODIC STRUCTURES
Electromagnetics, 1986
Calculation of High-Resolution SAR Distributions in Biological Bodies Using the FFT Algorithm and Conjugate Gradient Method (Short Papers)
IEEE Transactions on Microwave Theory and Techniques, 1985
The application of the conjugate gradient method for the solution of operator equations arising in electromagnetic scattering from wire antennas
Radio Science, 1984
Block Toeplitz Matrix Inversion
SIAM Journal on Applied Mathematics, 1973
The Toeplitz matrix: Its occurrence in antenna problems and a rapid inversion algorithm
IEEE Transactions on Antennas and Propagation, 1972