On the Influence of the Orthogonalization Scheme on the Parallel Performance of GMRES

In Krylov-based iterative methods, the computation of an orthonormal basis of the Krylov space is a key issue in the algorithms because the many scalar products are often a bottleneck in parallel distributed environments. Using GMRES, we present a comparison of four variants of the Gram-Schmidt process on distributed memory machines. Our experiments are carried on an application in astrophysics and on a convection-diiusion example. We show that the iterative classical Gram-Schmidt method overcomes its three competitors in speed and in parallel scalability while keeping robust numerical properties.