GMRES acceleration of iterative implicit finite element solvers for compressible Euler and Navier‐Stokes equations
Rémi Choquet, Pénélope Leyland, Tiana Tefy · International Journal for Numerical Methods in Fluids · 1995
Abstract Implicit iterative schemes based on linearized and non‐linear Newton methods are discussed, with resolution of a matrix subsystem or a matrix‐free method by preconditioned GMRES algorithms. The defaults of convergence due to the locality of Newton algorithms can be partially overcome by using stabilizing descent techniques, restarting and global strategies such as line search backtracking procedures, or by tuning the iterations once the approximate Jacobians are closer to the exact ones. Comparison with a more conventional relaxation method and their implementation on parallel architectures are discussed.