GMRES ACCELERATION OF ITERATIVE IMPLICIT FINITE-ELEMENT SOLVERS FOR COMPRESSIBLE EULER AND NAVIER-STOKES EQUATIONS

Implicit iterative schemes based on linearized and non-linear Newton m ethods are discussed, with resolution of a matrix subsystem or a matri x-free method by preconditioned GMRES algorithms. The defaults of conv ergence due to the locality of Newton algorithms can be partially over come by using stabilizing descent techniques, restarting and global st rategies such as line search backtracking procedures, or by tuning the iterations once the approximate Jacobians are closer to the exact one s. Comparison with a more conventional relaxation method and their imp lementation on parallel architectures are discussed.