Parallel conjugate gradient: effects of ordering strategies, programming paradigms, and architectural platforms

Conference · Mon May 01 04:00:00 EDT 2000

OSTI ID:775130

Oliker, L ^[1]; Li, X; Heber, G; Biswas, R

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1. LBNL Library

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. A sparse matrix-vector multiply (SPMV) usually accounts for most of the floating-point operations with a CG iteration. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and SPMV using different programming and architectures. Results show that for this class of applications, ordering significantly improves overall performance, that cache reuse may be more important than reducing communication, and that it is possible to achieve message passing performance using shared memory constructs through careful data ordering and distribution. However, a multithreaded implementation of CG on the Tera MTA does not require special ordering or partitioning to obtain high efficiency and scalability.

• Research Organization: Lawrence Berkeley National Lab., CA (US)
• Sponsoring Organization: USDOE Director, Office of Science. Office of Advanced Scientific Computing Research. Mathematical, Information, and Computational Sciences Division; National Aeronautics and Space Administration (US)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 775130
• Report Number(s): LBNL--45828
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
COMPUTER ARCHITECTURE
EFFICIENCY
IMPLEMENTATION
ITERATIVE METHODS
ORDERING ALGORITHMS UNSTRUCTURED MESHES SPARSE MATRICES DISTRIBUTED AND SHARED MEMORY MULTITHREADING
PARALLEL PROCESSING
PERFORMANCE