An Augmented Lagrangian Approach to Linearized Problems in Hydrodynamic Stability

Authors:
Maxim A. Olshanskii;Michele Benzi
Affiliations:
Maxim.Olshanskii@mtu-net.ru;benzi@mathcs.emory.edu
Venue:
SIAM Journal on Scientific Computing
Year:
2008

Citing 0
Cited 3

Spectral Analysis of Saddle Point Matrices with Indefinite Leading Blocks

SIAM Journal on Matrix Analysis and Applications
Field-of-Values Convergence Analysis of Augmented Lagrangian Preconditioners for the Linearized Navier-Stokes Problem

SIAM Journal on Numerical Analysis
Analysis of Augmented Lagrangian-Based Preconditioners for the Steady Incompressible Navier-Stokes Equations

SIAM Journal on Scientific Computing

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Abstract

The solution of linear systems arising from the linear stability analysis of solutions of the Navier-Stokes equations is considered. Due to indefiniteness of the submatrix corresponding to the velocities, these systems pose a serious challenge for iterative solution methods. In this paper, the augmented Lagrangian-based block triangular preconditioner introduced by the authors in [SIAM J. Sci. Comput., 28 (2006), pp. 2095-2113] is extended to this class of problems. We prove eigenvalue estimates for the velocity submatrix and deduce several representations of the Schur complement operator which are relevant to numerical properties of the augmented system. Numerical experiments on several model problems demonstrate the effectiveness and robustness of the preconditioner over a wide range of problem parameters.