MPI+OpenMP parallel implementation of conjugate gradient method with factored implicit preconditioners

Non-iterative algorithms based on MPI+OpenMP techniques are proposed for the construction and application of the Block Jacobi preconditioner combined with incomplete parameter-trimmed decomposition IC1 and stabilized incomplete parameter-trimmed decomposition IC2S. At the same time, the number of blocks in the Jacobi block is a multiple of the number of processors used and the number of threads used. Estimates of the number of iterations of conjugate gradients method with the Block Jacobi preconditioner combined with IC1 or IC2S methods obtained. Using model tasks calculations and a number of tasks from the sparse matrix collection SuiteSparse shown that the use of MPI+OpenMP technology makes it possible to significantly speed up calculations compared to the use of only MPI for not too many nodes of a supercomputer system.