Study of efficiency of several preconditioners for parallel solving sparse linear systems on graphics processors

Abstract

Performance evaluation of Intel Xeon CPUs and NVIDIA Tesla GPUs in solving of sparse linear systems using BiCGStab iteration method with BILU(0) preconditioner is performed; it is shown that using of GPUs allows to decrease linear solve time in 4,3–7,7 times. AIPS method approximating inverse matrix using Neumann power series and its applicability as first stage of two-stage CPR preconditioner is considered. Effectiveness evaluation of linear solve procedure with different preconditioners (BILU(0), CPR-AMG, CPR-AIPS) on computing system with two NVIDIA Tesla P100 GPUs is performed; it is shown that due to parallel implementation of AIPS method CPR-AIPS preconditioner has good scalability that leads to decrease of solve time for majority of test linear systems.