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Toward Auto-tuned Krylov Basis Computations with minimized Communication on Clusters of Accelerators

Langshi Chen, Serge Petiton, Leroy Drummond, Maxime Hugues
Maison de la Simulation, USR3441, Digiteo Labs Bat 565-PC 190, 91191 Gif-sur-Yvette, France
11th International Meeting High Performance Computing for Computational Science (VECPAR), 2014

@article{chen2014toward,

   title={Toward Auto-tuned Krylov Basis Computations with minimized Communication on Clusters of Accelerators},

   author={CHEN, Langshi and PETITON, Serge and DRUMMOND, Leroy and HUGUES, Maxime},

   year={2014}

}

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Krylov Subspace Methods (KSMs) are widely used for solving large scale linear systems and eigenproblems. However, the computing of Krylov subspace basis for KSMs suffers from its intensive blocking scalar product computation and communication, especially in large clusters with accelerators like GPUs. In this paper, a Hyper Graph based communication optimization is applied to Arnoldi and incomplete Arnoldi methods of forming Krylov basis, and we compare their performance with classic Arnoldi methods within a CPU-GPU framework. Results show the benefits from optimization and its drawbacks which require further integration of auto-tuning technologies.
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