Computer Methods in Applied Mechanics and Engineering
Matrix computations (3rd ed.)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Algorithm 837: AMD, an approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow
ACM Transactions on Mathematical Software (TOMS)
An Augmented Lagrangian-Based Approach to the Oseen Problem
SIAM Journal on Scientific Computing
Pressure Schur Complement Preconditioners for the Discrete Oseen Problem
SIAM Journal on Scientific Computing
Least Squares Preconditioners for Stabilized Discretizations of the Navier-Stokes Equations
SIAM Journal on Scientific Computing
An Augmented Lagrangian Approach to Linearized Problems in Hydrodynamic Stability
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
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We analyze a class of modified augmented Lagrangian-based preconditioners for both stable and stabilized finite element discretizations of the steady incompressible Navier-Stokes equations. We study the eigenvalues of the preconditioned matrices obtained from Picard linearization, and we devise a simple and effective method for the choice of the augmentation parameter $\gamma$ based on Fourier analysis. Numerical experiments on a wide range of model problems demonstrate the robustness of these preconditioners, yielding fast convergence independent of mesh size and only mildly dependent on viscosity on both uniform and stretched grids. Good results are also obtained on linear systems arising from Newton linearization. We also show that performing inexact preconditioner solves with an algebraic multigrid algorithm results in excellent scalability. Comparisons of the modified augmented Lagrangian preconditioners with other state-of-the-art techniques show the competitiveness of our approach.