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

Download

index.pdf

Date

2007-06-15

Author

Ergül, Özgür Salih

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

204
views

0
downloads

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 the improved convergence characteristics.

Subject Keywords

Integral equations, Iterative algorithms, Tin, Testing, Acceleration, MLFMA, Surface waves, Computational electromagnetics, Electromagnetic scattering, Computational geometry

URI

https://hdl.handle.net/11511/34358

DOI

https://doi.org/10.1109/aps.2007.4395880

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Accurate Solutions of Extremely Large Integral-Equation Problems in Computational Electromagnetics Ergül, Özgür Salih (2013-02-01) Accurate simulations of real-life electromagnetics problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be achieved easily, even when using the most powerful computers with state-of-the-art technology. However, with the multilevel fast multipole algorithm (MLFMA) and parallel MLFMA, we have been able to obtain full-wave solutions of scattering problems discretized with hundreds of millions of unknow...
Improving the accuracy of the MFIE with the choice of basis functions Ergül, Özgür Salih (2004-06-26) In the method-of-moments (MOM) and the fast-multipole-method (FMM) solutions of the electromagnetic scattering problems modeled by arbitrary planar triangulations, the magnetic-field integral equation (MFIE) can be observed to give less accurate results compared to the electric-field integral equation (EFIE), if the current is expanded with the Rao-Wilton-Glisson (RWG) basis functions. The inaccuracy is more evident for problem geometries with sharp edges or tips. This paper shows that the accuracy of the M...
Rigorous Solutions of Electromagnetic Problems Involving Hundreds of Millions of Unknowns Ergül, Özgür Salih (2011-02-01) Accurate simulations of real-life electromagnetic problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be easily achieved, even when using the most powerful computers with state-of-the-art technology. Hence, many electromagnetic problems in the literature have been solved by resorting to various approximation techniques, without controllable error. In this paper, we present full-wave solutions of sc...
Efficient solution of the combined-field integral equation with the parallel multilevel fast multipole algorithm Gürel, Levent; Ergül, Özgür Salih (2007-08-31) We present fast and accurate solutions of large-scale scattering problems formulated with the combined-field integral equation. Using the multilevel fast multipole algorithm (MLFMA) parallelized on a cluster of computers, we easily solve scattering problems that are discretized with tens of millions of unknowns. For the efficient parallelization of MLFMA, we propose a hierarchical partitioning scheme based on distributing the multilevel tree among the processors with an improved load-balancing. The accuracy...
Combined-field solution of composite geometries involving open and closed conducting surfaces Ergül, Özgür Salih (2005-04-07) Combined-field integral equation (CFIE) is modified and generalized to formulate the electromagnetic problems of composite geometries involving both open and closed conducting surfaces. These problems are customarily formulated with the electric-field integral equation (EFIE) due to the presence of the open surfaces. With the new definition and application of the CFIE, iterative solutions of these problems are now achieved with significantly improved efficiency compared to the EFIE solution, without sacrifi...

Citation Formats

Ö. S. Ergül, “Iterative solution of the normal-equations form of the electric-field integral equation,” 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34358.