MPI+OpenMP parallel implementation of conjugate gradient method with factorized preconditioner

Two non-iterative algorithms based on MPI+OpenMP techniques are proposed for the construction and application of the Block Jacobi preconditioner combined with IC(0) factorization. In the algorithms, OpenMP processing is used for almost all rows of the matrix. In Algorithm 1, the Domain Decomposition Ordering is used for the organization of OpenMP processing, while Algorithm 2 uses sparsification of matrix structure. Comparative timing results for the MPI+OpenMP and MPI implementations of the proposed preconditioning used with the conjugate gradient method for a model problem and the University of Florida collection test problems are presented.