Accelerating iterative linear solvers using multiple graphical processing units

Abstract

In this paper, we develop, study and implement iterative linear solvers and preconditioners using multiple graphical processing units (GPUs). Techniques for accelerating sparse matrix–vector (SpMV) multiplication, linear solvers and preconditioners are presented. Four Krylov subspace solvers, a Neumann polynomial preconditioner and a domain decomposition preconditioner are implemented. Our numerical tests with NVIDIA C2050 GPUs show that the SpMV kernel can be sped over 40 times faster using four GPUs. Our linear solvers and preconditioners have similar speedup.

Keywords:

• multi-GPUs
• SpMV
• linear solver
• domain decomposition preconditioner
• preconditioner
• parallel computing

2010 AMS Subject Classifications:

• 65Y05
• 68W10
• 65Y04

Acknowledgements

The support of Department of Chemical and Petroleum Engineering, University of Calgary and Reservoir Simulation Group is gratefully acknowledged. The research is partly supported by NSERC/AIEES/Foundation CMG and AITF Chairs.