Toward Auto-tuned Krylov Basis Computation for Different Sparse Matrix Formats and Interconnects on GPU Clusters

Krylov subspace methods (KSMs) are widely used in solving large-scale sparse linear problems. The orthogonalization process in methods like GMRES would consume a majority of the time. Since modern manycore architecture based accelerators have provided great horsepowers for computations,communication overheads remain a bottleneck, especially in clusters with a great number of nodes. The HA-PACS/TCA of Tsukuba University is a CPU-GPU hybrid cluster equipped with different interconnects for communications among GPUs. We testa group of Krylov basis computation methods with different sparse matrices and interconnects on HA-PACS/TCA. Results show that an auto-tuning scheme is required to deal with various types of matrices.