Efficient solution of the electric-field integral equation using the iterative LSQR algorithm

Download

index.pdf

Date

2008-01-01

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

266
views

0
downloads

In this letter, we consider iterative solutions of the three-dimensional electromagnetic scattering problems formulated by surface integral equations. We show that solutions of the electric-field integral equation (EFIE) can be improved by employing an iterative least-squares QR (LSQR) algorithm. Compared to many other Krylov subspace methods, LSQR provides faster convergence and it becomes an alternative choice to the time-efficient no-restart generalized minimal residual (GMRES) algorithm that requires large amounts of memory. Improvements obtained with the LSQR algorithm become significant for the solution of large-scale problems involving open surfaces that must be formulated using EFIE, which leads to matrix equations that are usually difficult to solve iteratively, even when the matrix-vector multiplications are accelerated via the multilevel fast multipole algorithm.

Subject Keywords

Electrical and Electronic Engineering

URI

https://hdl.handle.net/11511/41916

Journal

IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS

DOI

https://doi.org/10.1109/lawp.2007.908008

Collections

Department of Electrical and Electronics Engineering, Article

Suggestions

OpenMETU
Core

Fast and accurate solutions of extremely large integral-equation problems discretised with tens of millions of unknowns Gurel, L.; Ergül, Özgür Salih (Institution of Engineering and Technology (IET), 2007-04-26) The solution of extremely large scattering problems that are formulated by integral equations and discretised with tens of millions of unknowns is reported. Accurate and efficient solutions are performed by employing a parallel implementation of the multilevel fast multipole algorithm. The effectiveness of the implementation is demonstrated on a sphere problem containing more than 33 million unknowns, which is the largest integral-equation problem ever solved to our knowledge.
Implementation of the Equivalence Principle Algorithm for Potential Integral Equations Farshkaran, Ali; Ergül, Özgür Salih (Institute of Electrical and Electronics Engineers (IEEE), 2019-05-01) A novel implementation of the equivalence principle algorithm (EPA) employing potential integral equations (PIEs) is presented. EPA is generalized to be compatible with PIEs that are used to formulate inner problems inside equivalence surfaces. Based on the stability of PIEs, the resulting EPA-PIE implementation is suitable for low-frequency problems involving dense discretizations with respect to wavelength. Along with the formulation and a clear demonstration of the EPA-PIE mechanism, high accuracy, stabi...
Efficient parallelization of the multilevel fast multipole algorithm for the solution of large-scale scattering problems Ergül, Özgür Salih (Institute of Electrical and Electronics Engineers (IEEE), 2008-08-01) We present fast and accurate solutions of large-scale scattering problems involving three-dimensional closed conductors with arbitrary shapes using the multilevel fast multipole algorithm (MLFMA). With an efficient parallelization of MLFMA, scattering problems that are discretized with tens of millions of unknowns are easily solved on a cluster of computers. We extensively investigate the parallelization of MLFMA, identify the bottlenecks, and provide remedial procedures to improve the efficiency of the imp...
Contamination of the Accuracy of the Combined-Field Integral Equation With the Discretization Error of the Magnetic-Field Integral Equation Gurel, Levent; Ergül, Özgür Salih (Institute of Electrical and Electronics Engineers (IEEE), 2009-09-01) We investigate the accuracy of the combined-field integral equation (CFIE) discretized with the Rao-Wilton-Glisson (RWG) basis functions for the solution of scattering and radiation problems involving three-dimensional conducting objects. Such a low-order discretization with the RWG functions renders the two components of CFIE, i.e., the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE), incompatible, mainly because of the excessive discretization error of MFIE. Solutio...
Use of Asymptotic Waveform Evaluation Technique in the Analysis of Multilayer Structures With Doubly Periodic Dielectric Gratings Gudu, Tamer; Alatan, Lale (Institute of Electrical and Electronics Engineers (IEEE), 2009-09-01) The reflection and dispersion characteristics of multilayer structures that involve periodically implanted material blocks are obtained by using the MoM solution of the volume integral equation. The asymptotic waveform evaluation (AWE) technique is utilized to obtain a Pade approximation of the solution in terms of a parameter such as frequency or incident angle. The use of AWE technique enables a fast sweep with respect to the approximation parameter. Moreover, a robust method for extracting the dispersion...

Citation Formats

Ö. S. Ergül, “Efficient solution of the electric-field integral equation using the iterative LSQR algorithm,” IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, pp. 36–39, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41916.