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GMRES acceleration of iterative implicit finite element solvers for compressible Euler and Navier‐Stokes equations
Author(s) -
Choquet Rémi,
Leyland Pénélope,
Tefy Tiana
Publication year - 1995
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650200816
Subject(s) - generalized minimal residual method , mathematics , finite element method , backward euler method , convergence (economics) , relaxation (psychology) , iterative method , euler's formula , newton's method , line search , euler equations , mathematical optimization , computer science , mathematical analysis , nonlinear system , radius , psychology , social psychology , physics , computer security , quantum mechanics , economics , thermodynamics , economic growth
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.