Premium
An efficient solution of a dense system of linear equations arising in the method‐of‐moments formulation
Author(s) -
Prakash V. V. S.,
Kwon Soon Jae,
Mittra Raj
Publication year - 2002
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.10274
Subject(s) - generalized minimal residual method , conjugate gradient method , mathematics , linear system , method of moments (probability theory) , iterative method , residual , convergence (economics) , matrix (chemical analysis) , rank (graph theory) , factorization , system of linear equations , microwave , simple (philosophy) , computer science , mathematical optimization , mathematical analysis , algorithm , materials science , telecommunications , statistics , combinatorics , estimator , economics , composite material , economic growth , philosophy , epistemology
This Letter presents a simple and efficient approach for preconditioning a large dense system of linear equations arising in the method‐of‐moments (MoM) solution of electromagnetic (EM) problems. A two‐step process is presented in which the condition number of the matrix is first improved by equilibration, and then further enhanced by preconditioning. The convergence properties of two frequently used iterative solvers, namely, the conjugate‐gradient normal (CGNR) and the generalized minimal residual (GMRES) methods, have been studied with the use of the proposed technique, and the efficacy of the method has been compared with that of the direct LU factorization. The Letter demonstrates that the proposed technique helps improve the computational efficiency of the iterative solvers considerably, not only for MoM matrices associated with electrically large geometries, but also for poorly conditioned matrices with a relatively small rank. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 196–200, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10274