Minimizing synchronizations in sparse iterative solvers for distributed supercomputers

Eliminating synchronizations is one of the important techniques related to minimizing communications for modern high performance computing. This paper discusses principles of reducing communications due to global synchronizations in sparse iterative solvers on distributed supercomputers. We demonstrate how to minimize global synchronizations by rescheduling a typical Krylov subspace method. The benefit of minimizing synchronizations is shown in theoretical analysis and verified by numerical experiments. The experiments also show the local communications for some structured sparse matrix–vector multiplications and global communications in the underlying supercomputers increase in the order P1/2.5P1/2.5 and P4/5P4/5 respectively, where PP is the number of processors.