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.
iterative solution of linear systems, sparse matrices, incomplete inverse triangular factorization, parallel preconditioning, BiCGStab method