MPI+OpenMP parallel implementation of conjugate gradient method with the Block Jacobi preconditioner combined with IC1

Two 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. In Algorithm 1, the Domain Decomposition Ordering is used for the organization of OpenMP processing, OpenMP processing is used for almost all rows of the matrix. In Algorithm 2 uses sparsification of matrix structure, OpenMP processing is used for all rows of the matrix. 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.