Lower bounds for three-dimensional nonoverlapping domain decomposition algorithms
type: Item
instance of: scholarly article
title: Lower bounds for three-dimensional nonoverlapping domain decomposition algorithms
zbMATH Open document ID: 1054.65043
author: Susanne C. Brenner
author: Qingmi He
published in: Numerische Mathematik
publication date: 2003-03-18T00:00:00Z
review text: The authors show that the known upper bounds of the wire basket preconditioner and the Neumann-Neumann preconditioner in three dimensions for nonoverlapping domain decomposition algorithms are sharp. The proof for the wire basket preconditioner is based on finding that the upper bound of \(\lambda_{\min}\) is of the same order than the known lower bound, and the lower bound of \(\lambda_{\max}\) is \(1\). Then, the condition number for this preconditioner is bounded below and above for the same quantity. The same procedure follows for the Neumann-Neumann preconditioner where in this case \(1\) is an upper bound of \(\lambda_{\min}\), and the lower bound of \(\lambda_{\max}\) is of the same order than the known upper bound.
reviewed by: J. Mas
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1884039
zbMATH Keywords: domain decomposition methods
zbMATH Keywords: basket preconditioner
zbMATH Keywords: Neumann-Neumann preconditioner
MaRDI profile type: Publication
full work available at URL: s002110100376
OpenAlex ID: W1967581090
DOI: 10.1007/S002110100376
description: scientific article; zbMATH DE number 1884039