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Incomplete Sparse Approximate Inverses (ISAI) has shown some advantages over sparse triangular solves on GPUs when it is used for the incomplete LU based preconditioner. In this paper, we extend the single GPU method for Block–ISAI to multiple GPUs algorithm by coupling Block–Jacobi preconditioner, and introduce the detailed implementation in the open source numerical package PETSc. In the experiments, two representative cases are performed and a comparative study of Block–ISAI on up to four GPUs are conducted on two major generations of NVIDIA’s GPUs (Tesla K20 and Tesla V100). Block–Jacobi preconditioning with Block–ISAI (BJPB-ISAI) shows an advantage over the level-scheduling based triangular solves from the cuSPARSE library for the cases, and the overhead of setting up Block–ISAI and the total wall clock times of GMRES is greatly reduced using Tesla V100 GPUs compared to Tesla K20 GPUs.

A Comparative Study of Block Incomplete Sparse Approximate Inverses Preconditioning on Tesla K20 and V100 GPUs