Premium
Incomplete factorization‐based preconditionings for solving the Helmholtz equation
Author(s) -
Magolu Monga Made Mardochée
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/1097-0207(20010220)50:5<1077::aid-nme65>3.0.co;2-p
Subject(s) - preconditioner , incomplete cholesky factorization , mathematics , factorization , matrix decomposition , incomplete lu factorization , generalized minimal residual method , matrix (chemical analysis) , diagonal , condition number , linear system , positive definite matrix , sparse matrix , iterative method , mathematical analysis , algorithm , eigenvalues and eigenvectors , geometry , physics , materials science , quantum mechanics , composite material , gaussian
Preconditioning techniques based on incomplete factorization of matrices are investigated, to solve highly indefinite complex‐symmetric linear systems. A novel preconditioning is introduced. The real part of the matrix is made positive definite, or less indefinite, by adding properly defined perturbations to the diagonal entries, while the imaginary part is unaltered. The resulting preconditioning matrix, which is obtained by applying standard methods to the perturbed complex matrix, turns out to perform significantly better than classical incomplete factorization schemes. For realistic values of the GMRES restart parameter, spectacular reduction of iteration counts is observed. A theoretical spectral analysis is provided, in which the spectrum of the preconditioner applied to indefinite matrix is related to the spectrum of the same preconditioner applied to a Stieltjes matrix extracted from the indefinite matrix. Results of numerical experiments are reported, which display the efficiency of the new preconditioning. Copyright © 2001 John Wiley & Sons, Ltd.