Parallel GMRES Incomplete Orthogonalization Auto-Tuning
Pierre-Yves Aquilanti, Serge G. Petiton, Henri Calandra · Procedia Computer Science · 2011
Krylov linear solvers are widely used to solve various kind of scientific problems. They are entitled to many optimization in order to reduce the processing time needed to attain solution. However, these optimisations are mainly problems specific and do not always fit well in parallel. Tuning them can sometimes require and heavy work to extract sustainable performances. Auto-tuning helps the users to tune their solver with little e_ort and at a small cost. We present a general parallel auto-tuned linear solver approach in order to reduce the time of computation needed for a solver to attain solution. Our new approach is based on the tuning of the Arnoldi incomplete orthogonalization process within GMRES by monitoring the convergence thanks to a simple heuristic. We obtained promising results by reducing significantly the time of computation on di_erent cases in serial and parallel processing using a cluster, involving both real and complex valued linear systems. Our work enlight the emergence of incomplete Arnoldi orthogonalization auto-tuning as a possible optimization for iteratives methods.