Preconditioning of discrete Helmholtz operators perturbed by a diagonal complex matrix

✍ Scribed by Magolu monga Made, Mardoch�e ;Beauwens, Robert ;Warz�e, Guy

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 190 KB
• Volume: 16
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/1099-0887(200011)16:11<801::aid-cnm377>3.0.co;2-m

✦ Synopsis

Incomplete factorizations are popular preconditioning techniques for solving large and sparse linear systems. In the case of highly indeÿnite complex-symmetric linear systems, the convergence of Krylov subspace methods sometimes degrades with increasing level of ÿll-in. The reasons for this disappointing behaviour are twofold. On the one hand, the eigenvalues of the preconditioned system tend to 1, but the 'convergence' is not monotonous. On the other hand, the eigenvalues with negative real part, on their move towards 1 have to cross the origin, whence the risk of clustering eigenvalues around 0 while 'improving' the preconditioner. This makes it risky to predict any gain when passing from a level to a higher one. We examine a remedy which consists in slightly moving the spectrum of the original system matrix along the imaginary axis. Theoretical analysis that motivates our approach and experimental results are presented, which displays the e ciency of the new preconditioning techniques.