Mpi+openmp implementation of conjugate gradients method with preconditioner of the block incomplete inverse triangular decomposition of the first order

The paper considers the preconditioner of the block incomplete inverse triangular decomposition of the first order “by value” BIIC-IC1 for solving systems of linear algebraic equations with a symmetric positively defined matrix. A method of using MPI+OpenMP technology for constructing and inverting the BIIC-IC1 preconditioner, in which the number of blocks in the preconditioner is a multiple of the number of used processors and used threads, is considered. A method is proposed for using the MPI+OpenMP technology to construct and invert the BIICIC1 preconditioner, in which a special ordering of grid nodes within subdomains corresponding to processor calculations is used to apply the OpenMP technology. The time of solving problems by the conjugate gradient method with the BIIC-IC1 preconditioner using MPI and hybrid MPI + OpenMP technology is compared on the example of a model problem and a number of problems from the collection of sparse matrices SuiteSparse.