Efficient parallel sparse Cholesky factorization

Conference · Fri Dec 01 04:00:00 EST 1995

OSTI ID:125543

Rothberg, E ^[1]; Schreiber, R ^[2]

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1. Silicon Graphics, Inc., Mountain View, CA (United States)
2. NASA Ames Research Center, Moffett Field, CA (United States)

Scalable implementations of sparse Cholesky factorization use block mappings of the dense parts of the matrix onto a 2-D processor grid, mappings which reduce communication cost. With naive cyclic mappings, block-oriented approaches (specifically, the block fan-out method) suffer from poor balance of the computational load and modest efficiency. Here, we show that heuristic remapping of the block rows and columns essentially removes load imbalance as a cause of inefficiency, producing a 20% increase in realized performance on a 196-node Paragon multicomputer. To attack the remaining inefficiency, we consider the scheduling of available tasks at each node. Priorities based on elimination tree depth yield another 10% improvement.

• OSTI ID: 125543
• Report Number(s): CONF-950212--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
FACTORIZATION
MATRICES
NUMERICAL SOLUTION
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS