A parallel preconditioner based on the approximation of an inverse matrix by power series for solving sparse linear systems on graphics processors

The applicability of the AIPS method approximating an inverse matrix using Neumann series is considered in the framework of the CPR two stage preconditioner. A parallel CUDA-oriented algorithm is proposed for solving linear systems with tridiagonal matrices consisting of independent blocks of different sizes. It is shown that the implementation of the proposed algorithm can be more than twice the speed of the similar functions from the cuSPARSE library. Experimental evaluation of the BiCGStab method with the CPR-AIPS preconditioner on modern GPUs, including a hybrid computing system with 4 GPU NVIDIA Tesla V100, is performed. Numerical experiments show an adequate scalability of this preconditioner as well as the possibility (compared to the CPR-AMG) to accelerate the solution of linear systems being typical for the reservoir modeling problems.