Iterative methods for the solution of elliptic problems on regions partitioned into substructures
SIAM Journal on Numerical Analysis
A domain decomposition technique for Stokes problems
Applied Numerical Mathematics - Domain Decomposition
Stable Numerical Algorithms for Equilibrium Systems
SIAM Journal on Matrix Analysis and Applications
An Adaptive Newton--Picard Algorithm with Subspace Iteration for Computing Periodic Solutions
SIAM Journal on Scientific Computing
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Matrix Renumbering ILU: An Effective Algebraic Multilevel ILU Preconditioner for Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization
SIAM Journal on Scientific Computing
A Preconditioner for the Steady-State Navier--Stokes Equations
SIAM Journal on Scientific Computing
A Note on the LDLT Decomposition of Matrices from Saddle-Point Problems
SIAM Journal on Matrix Analysis and Applications
Bifurcation analysis of incompressible flow in a driven cavity by the Newton-Picard method
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Symmetry-preserving discretization of turbulent flow
Journal of Computational Physics
The performance of implicit ocean models on B- and C-grids
Journal of Computational Physics
Journal of Computational Physics
An Augmented Lagrangian-Based Approach to the Oseen Problem
SIAM Journal on Scientific Computing
A Parallel Multistage ILU Factorization Based on a Hierarchical Graph Decomposition
SIAM Journal on Scientific Computing
A Parallel Direct/Iterative Solver Based on a Schur Complement Approach
CSE '08 Proceedings of the 2008 11th IEEE International Conference on Computational Science and Engineering
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We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method introduced here has the following properties: (i) it is very robust, even close to the point where the solution becomes unstable; (ii) a single parameter controls fill and convergence, making the method straightforward to use; (iii) the convergence rate is independent of the number of unknowns; (iv) it can be implemented on distributed memory machines in a natural way; (v) the matrix on the second level has the same structure and numerical properties as the original problem, so the method can be applied recursively; (vi) the iteration takes place in the divergence-free space, so the method qualifies as a “constraint preconditioner”; (vii) the approach can also be applied to Poisson problems. This work is also relevant for problems in which similar saddle point matrices occur, for instance, when simulating electrical networks, where one has to satisfy Kirchhoff's conservation law for currents.