Parallel implementation of an efficient preconditioned linear solver for grid-based applications in chemical physics. III: Improved parallel scalability for sparse matrix-vector products

The linear solve problems arising in chemical physics and many other fields involve large sparse matrices with a certain block structure, for which special block Jacobi preconditioners are found to be very efficient. In two previous papers [W. Chen, B. Poirier, Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. I. Block Jacobi diagonalization, J. Comput. Phys. 219 (1) (2006) 185-197; W. Chen, B. Poirier, Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. II. QMR linear solver, J. Comput. Phys. 219 (1) (2006) 198-209], a parallel implementation was presented. Excellent parallel scalability was observed for preconditioner construction, but not for the matrix-vector product itself. In this paper, we introduce a new algorithm with (1) greatly improved parallel scalability and (2) generalization for arbitrary number of nodes and data sizes.