Sparse direct solution on parallel computers
type: Item
instance of: scholarly article
title: Sparse direct solution on parallel computers
zbMATH Open document ID: 1478.65032
DOI: 10.1007/978-3-319-90026-1_4
author: Florent Lopez
author: Stojce Nakov
author: Iain S. Duff
publication date: 2018-11-30T00:00:00Z
full work available at URL: http://purl.org/net/epubs/work/34746569
review text: This paper discusses designing algorithms and software for solving sparse systems using direct methods on parallel computers. After discussing the solution of large sparse symmetric positive definite systems, the authors use a runtime system to express and execute a DAG (directed acyclic graphs)-based Cholesky factorization. The runtime system plays the role of a software layer between the application and the architecture and handles the management of task dependencies as well as task scheduling and maintaining data coherency. The software is implemented using the OpenMP standard and the runtime systems StarPU and PaRSEC. The performance is demonstrated on a multicore architecture. The case of symmetric indefinite matrix is also considered. For highly unsymmetrical systems, a completely different approach based on developing a parallel version of a Markowitz threshold ordering is used where some of the algorithmic challenges involved are discussed. Finally, using a hybrid direct-iterative solver that combines the better of the two approaches that enables the solution of even larger problems in parallel is described. For the entire collection see [Zbl 1402.65005].
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65-04
zbMATH DE Number: 6987052
zbMATH Keywords: sparse symmetric systems
zbMATH Keywords: unsymmetric sparse systems
zbMATH Keywords: direct methods
zbMATH Keywords: hybrid methods
zbMATH Keywords: runtime systems
zbMATH Keywords: block Cimmino
zbMATH Keywords: Markowitz threshold
describes a project that uses: MA48
describes a project that uses: HSL_MA97
describes a project that uses: SparseMatrix
describes a project that uses: StarPU
MaRDI profile type: Publication
OpenAlex ID: W2806173155
description: scientific article; zbMATH DE number 6987052