A parallel sparse approximate inverse preconditioning algorithm based on MPI and CUDA

In this study, we present an efficient parallel sparse approximate inverse (SPAI) preconditioning algorithm based on MPI and CUDA, called HybridSPAI. For HybridSPAI, it optimizes a latest static SPAI preconditioning algorithm, and is extended from one GPU to multiple GPUs in order to process large-scale matrices. We make the following significant contributions: (1) a general parallel framework for optimizing the static SPAI preconditioner based on MPI and CUDA is presented, and (2) for each component of the preconditioner, a decision tree is established to choose the optimal kernel of computing it. Experimental results show that HybridSPAI is effective, and outperforms the popular preconditioning algorithms in two public libraries, and a latest parallel SPAI preconditioning algorithm.