Premium
Spectral analysis of parallel incomplete factorizations with implicit pseudo‐overlap
Author(s) -
Magolu monga Made M.,
van der Vorst Henk A.
Publication year - 2001
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.247
Subject(s) - preconditioner , domain decomposition methods , locality , matrix decomposition , mathematics , convergence (economics) , factorization , parallelism (grammar) , contrast (vision) , algebraic number , qr decomposition , domain (mathematical analysis) , computer science , algorithm , parallel computing , iterative method , eigenvalues and eigenvectors , finite element method , mathematical analysis , linguistics , philosophy , physics , quantum mechanics , artificial intelligence , economics , thermodynamics , economic growth
Abstract Two general parallel incomplete factorization strategies are investigated. The techniques may be interpreted as generalized domain decomposition methods. In contrast to classical domain decomposition methods, adjacent subdomains exchange data during the construction of the incomplete factorization matrix, as well as during each local forward elimination and each local backward elimination involved in the application of the preconditioner. Local renumberings of nodes are combined with suitable global fill‐in strategy in an (successful) attempt to overcome the well‐known trade‐off between high parallelism (locality) and fast convergence (globality). From an algebraic viewpoint, our techniques may be implemented as global renumbering strategies. Theoretical spectral analysis is provided, which displays that the convergence rate weakly depends on the number of subdomains. Numerical results obtained on a 16‐processor SGI Origin 2000 are reported, showing the efficiency of our parallel preconditionings. Copyright © 2001 John Wiley & Sons, Ltd.