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Full Record Details
DOI
10.5286/raltr.2009027
Persistent URL
http://purl.org/net/epubs/work/51895
Record Status
Checked
Record Id
51895
Title
Design of a multicore sparse Cholesky factorization using DAGs
Contributors
JD Hogg
,
JK Reid (STFC Rutherford Appleton Lab.)
,
JA Scott (STFC Rutherford Appleton Lab.)
Abstract
The rapid emergence of multicore machines has led to the need to design new algorithms that are efficient on these architectures. Here, we consider the solution of sparse symmetric positive-definitive linear systems by Cholesky factorization. We were motivated by the successful division of the computation in the dense case into tasks on blocks and use of a task manager to exploit all the parallelism that is available between these tasks , whose dependencies may be represented by a directed acyclic graph (DAG). Our algorithm is built on the assembly tree and subdivides the work at each node into tasks on blocks, whose dependencies may again be represented by a DAG. To limit memory requirements, updates of blocks are performed directly. Our algorithm is implemented within a new solver HSL_MA87. It is written in Fortran 95 plus OpenMP and is avalable as part of the software library HSL. Using problems arising from a range of practical applications, we present experimental results that support our design choices and demonstrate HSL_MA87 obtains good serial and parallel times on our 8-core test machines. Comparisons are made with existing modern solvers and show that HSL_MA876 generally outperforms these solvers, particularly in the case of very large problems.
Organisation
CSE
,
CSE-NAG
,
STFC
Keywords
Fortran 95
,
parallel
,
Cholesky factorization
,
sparse symmetric linear systems
,
DAG-based
,
multicore
,
OpenMP
Funding Information
Related Research Object(s):
49215922
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Report
RAL Technical Reports
RAL-TR-2009-027. STFC, 2009.
hrsRALTR2009027.pdf
2009
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