Parallel hybrid algebraic multilevel iterative methods
type: Item
instance of: scholarly article
title: Parallel hybrid algebraic multilevel iterative methods
zbMATH Open document ID: 0891.65033
DOI: 10.1016/S0024-3795(97)80054-7
published in: Linear Algebra and its Applications
publication date: 1998-07-03T00:00:00Z
review text: An optimal preconditioner for systems of linear equations with a symmetric positive definite block coefficient matrix is presented. This preconditioner is blockdiagonal, and each block is defined by an algebraic multilevel iteration (AMLI) preconditioner [see, e.g., \textit{O. Axelsson} and \textit{P. S. Vassilevski}, SIAM J. Numer. Anal. 27, No. 6, 1569-1590 (1990; Zbl 0715.65091); \textit{P. S. Vassilevski}, Math. Comput. 58, No. 198, 489-512 (1992; Zbl 0765.65044)]. Within the AMLI preconditioners a polynomial of order \(\nu > 1\) is used for the approximation of the corresponding Schur complement on the levels \(k = sk_0 + 1\) (\(k_0\) is an appropriately chosen parameter, \(s = 1,2, \ldots , l/k_0 - 1\), \(l\) is the number of levels). On all other levels a polynomial of first order is utilized. It is shown that the convergence rate of iterative solvers with this preconditioner is independent of the number of levels used. The cost of arithmetical work is proportional to the number of unknowns on the finest level. Because of the block structure of the preconditioner its parallelization is obvious.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65N55
zbMATH DE Number: 1089501
zbMATH Keywords: iterative methods
zbMATH Keywords: multilevel methods
zbMATH Keywords: preconditioners
zbMATH Keywords: parallel computation
author: Zhong-Zhi Bai
reviewed by: Michael Jung
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1089501