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Modified augmented Lagrangian preconditioners for the incompressible Navier–Stokes equations
Author(s) -
Benzi Michele,
Olshanskii Maxim A.,
Wang Zhen
Publication year - 2011
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.2267
Subject(s) - preconditioner , augmented lagrangian method , generalized minimal residual method , finite element method , mathematics , convergence (economics) , block (permutation group theory) , navier–stokes equations , compressibility , lagrangian , linear system , mathematical optimization , mathematical analysis , geometry , physics , mechanics , economics , thermodynamics , economic growth
We study different variants of the augmented Lagrangian (AL)‐based block‐triangular preconditioner introduced by the first two authors in [ SIAM J. Sci. Comput. 2006; 28 : 2095–2113]. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual method (GMRES) applied to various finite element and Marker‐and‐Cell discretizations of the Oseen problem in two and three space dimensions. Both steady and unsteady problems are considered. Numerical experiments show the effectiveness of the proposed preconditioners for a wide range of problem parameters. Implementation on parallel architectures is also considered. The AL‐based approach is further generalized to deal with linear systems from stabilized finite element discretizations. Copyright © 2010 John Wiley & Sons, Ltd.