Iterative-method performance evaluation for multiple vectors associated with a large-scale sparse matrix

ABSTRACT

Ensemble computing, which is an instance of capacity computing, is an effective computing scenario for exascale parallel supercomputers. In ensemble computing, there are multiple linear systems associated with a common coefficient matrix. We improve the performance of iterative solvers for multiple vectors by solving them at the same time, that is, by solving for the product of the matrices. We implemented several iterative methods and compared their performance. The maximum performance on Sparc VIIIfx was 7.6 times higher than that of a naïve implementation. Finally, to deal with the different convergence processes of linear systems, we introduced a control method to eliminate the calculation of already converged vectors.

KEYWORDS:

• Ensemble computation
• iterative solver
• capacity computing
• sparse matrix
• high-performance computing

Acknowledgements

This research is supported in part by the RIKEN Advanced Institute for Computational Science, which allowed us to use the K computer to obtain our results.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. on Sparc VIIIfx, we count one flop each for addition, subtraction, and multiplication operators, and eight flops for a division operator.

Additional information

Funding

This work was supported in part by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) as a social and scientific priority issue (Development of Innovative Design and Production Processes that Lead the Way for the Manufacturing Industry in the Near Future) to be tackled by using post-K computer and KAKENHI [grant number (B) 26286087].