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Modified augmented Lagrangian preconditioners for the incompressible Navier-Stokes equations. (English) Zbl 1421.76152

Summary: We study different variants of the augmented Lagrangian (AL)-based block-triangular preconditioner introduced by the first two authors in [SIAM J. Sci. Comput. 28, No. 6, 2095–2113 (2006; Zbl 1126.76028)]. 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.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids

Citations:

Zbl 1126.76028

Software:

IFISS; Trilinos
PDFBibTeX XMLCite
Full Text: DOI

References:

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