A scalable multisplitting algorithm to solve large sparse linear systems

In this paper, we revisit the Krylov multisplitting algorithm presented in Huang and O'Leary (Linear Algebra Appl 194:9-29, 1993) which uses a sequential method to minimize the Krylov iterations computed by a multisplitting algorithm. Our new algorithm is based on a parallel multisplitting algorithm with few blocks of large size using a parallel GMRES method inside each block and on a parallel Krylov minimization to improve the convergence. Some large-scale experiments with a 3D Poisson problem are presented with up to 8,192 cores. They show the obtained improvements compared to a classical GMRES both in terms of number of iterations and in terms of execution times.