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ℋ-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systems
Publikationstyp
Journal Article
Date Issued
2010-12-09
Sprache
English
Author(s)
Institut
TORE-URI
Volume
68
Issue
1
Start Page
83
End Page
98
Citation
International Journal for Numerical Methods in Fluids 1 (68): 83-98 (2010)
Publisher DOI
Publisher
Wiley
The (mixed finite element) discretization of the linearized Navier-Stokes equations leads to a linear system of equations of saddle point type. The iterative solution of this linear system requires the construction of suitable preconditioners, especially in the case of high Reynolds numbers. In the past, a stabilizing approach has been suggested which does not change the exact solution but influences the accuracy of the discrete solution as well as the effectiveness of iterative solvers. This stabilization technique can be performed on the continuous side before the discretization, where it is known as 'grad-div' (GD) stabilization, as well as on the discrete side where it is known as an 'augmented Lagrangian' (AL) technique (and does not change the discrete solution). In this paper, we study the applicability of ℋ-LU factorizations to solve the arising subproblems in the different variants of stabilized saddle point systems. We consider both the saddle point systems that arise from the stabilization in the continuous as well as on the discrete setting. Recently, a modified AL preconditioner has been proposed for the system resulting from the discrete stabilization. We provide a straightforward generalization of this approach to the GD stabilization. We conclude the paper with numerical tests for a variety of problems to illustrate the behavior of the considered preconditioners as well as the suitability of ℋ-LU factorization in the preconditioners.
Subjects
ℋ-LU
augmented lagrangian method
grad-div stabilization
hierarchical matrices
oseen problem
saddle point problems
DDC Class
510: Mathematik