The reordered BiCGStab method for distributed memory computer systems

A new reordered formulation of the preconditioned BiCGStab iterative method for the system of linear equations with large sparse nonsymmetric matrix is presented. The algorithm is reformulated in order to improve the efficiency on distributed memory computer systems. It allows to avoid all global synchronization points of the inner product operations. The order of computations permits to overlap the communication time of the inner products by the preconditioning computations. The efficiency of the implemented method with the algebraic multigrid preconditioner is demonstrated by the scalability results for the MPI and the hybrid (MPI +SHM) programming models.