MPI+OpenMP parallel implementation of explicitly preconditioned conjugate gradient method

A preconditioner for large sparse symmetric positive definite coefficient matrix is considered based on its approximate inverse in the form of product of a lower triangular sparse matrix by its transpose. A parallel algorithm for the construction and application of the preconditioner is proposed with the use of MPI+OpenMP techniques. Comparative timing results for the MPI+OpenMP and MPI implementations of the considered preconditioning and the Jacobi preconditioning used with the conjugate gradient method for a model problem and the University of Florida collection test problems is presented.