MPI+OpenMP implementation of BiCGStab method with factorized explicit preconditioner

A preconditioner for large sparse nonsymmetric positive definite coefficient matrix is considered based on its approximate inverse in the form of product of a lower triangular sparse matrix by an upper triangular matrix. For the class of matrices considered, a new preconditioning based on approximate block Jacobi with incomplete inverse LU-factorization preconditioning is proposed. For parallel implementation of the corresponding preconditioned BiCGStab algorithm, the MPI+OpenMP techniques were used. Comparative timing results for the MPI+OpenMP and MPI implementations of the proposed preconditioning and the Jacobi preconditioning used with the BiCGStab for several test problems from the University of Florida sparse matrix collection are presented.