Macro-elementwise preconditioning methods
type: Item
instance of: scholarly article
title: Macro-elementwise preconditioning methods
zbMATH Open document ID: 1262.65045
author: Owe Axelsson
published in: Mathematics and Computers in Simulation
publication date: 2012-11-15T00:00:00Z
review text: For extremely large scale models derived from partial differential equations for heterogeneous media, macro- and micro-preconditioning are discussed. Grouping the variables into macro- and even micro-elements here allows for better modeling and more efficient parallel methods and even for different modeling methods for different portions of the variables. With a system partitioned according to its macro-elements, preconditioners must reflect this and be joined across their elementwise boundaries to ensure their efficiency. This leads to finding good approximate inverses for 2 by 2 block matrix preconditioners via approximate Schur complements for the \((2,1)\) block. The paper considers several incomplete Schur complements in this context and studies their effect on conditioning. Also elementwise approximations for such Schur complements are studied.
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 6107071
zbMATH Keywords: heterogeneous model
zbMATH Keywords: macro-elements
zbMATH Keywords: very large linear system
zbMATH Keywords: block matrix partitioning
zbMATH Keywords: macro-elementwise preconditioning
zbMATH Keywords: parallel computation
zbMATH Keywords: Schur complements
MaRDI profile type: Publication
full work available at URL: j.matcom.2012.06.006
OpenAlex ID: W1985439145
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DOI: 10.1016/J.MATCOM.2012.06.006
description: scientific article; zbMATH DE number 6107071