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On nonlinear preconditioners in Newton–Krylov methods for unsteady flows
Author(s) -
Birken Philipp,
Jameson Antony
Publication year - 2009
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.2030
Subject(s) - convergence (economics) , mathematics , newton's method , nonlinear system , operator (biology) , time stepping , matrix (chemical analysis) , scheme (mathematics) , computer science , mathematical analysis , physics , discretization , materials science , biochemistry , chemistry , repressor , quantum mechanics , economics , composite material , gene , economic growth , transcription factor
The application of nonlinear schemes like dual time stepping as preconditioners in matrix‐free Newton–Krylov‐solvers is considered and analyzed, with a special emphasis on unsteady viscous flows. We provide a novel formulation of the left preconditioned operator that says it is in fact linear in the matrix‐free sense, but changes the Newton scheme. This allows to get some insight in the convergence properties of these schemes, which is demonstrated through numerical results. Copyright © 2009 John Wiley & Sons, Ltd.