HeuriSPAI: a heuristic sparse approximate inverse preconditioning algorithm on GPU

In this study, we present a new heuristic sparse approximate inverse (SPAI) preconditioning algorithm on graphics processing unit (GPU), called HeuriSPAI. For the proposed HeuriSPAI, there are the following novelties: (1) a heuristic method is proposed, which gives the potential candidate indices of the nonzero entries of the preconditioner in advance to guide the selection of the new indices, so as to improve the quality of the obtained preconditioner; and (2) a parallel framework of constructing the heuristic SPAI preconditioner on GPU is presented on the basis of the new proposed heuristic SPAI preconditioning algorithm; and (3) each component of the preconditioner is computed in parallel inside a group of threads. HeuriSPAI fuses the advantages of static and dynamic SPAI preconditioning algorithms, and alleviates the drawback of the existing dynamic SPAI preconditioning algorithms on GPU that are not suitable for large matrices. Experimental results show that HeuriSPAI is effective for large matrices, and outperforms the popular preconditioning algorithms in three public libraries, as well as a recent parallel static SPAI preconditioning algorithm.