Preconditioning Methods for Linear Systems with Saddle Point Matrices
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Robust Preconditioners for Saddle Point Problems
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
A parallel solver for PDE systems and application to the incompressible Navier-Stokes equations
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
Analysis of iterative algorithms of Uzawa type for saddle point problems
Applied Numerical Mathematics
Preconditioning Strategies for Models of Incompressible Flow
Journal of Scientific Computing
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow
ACM Transactions on Mathematical Software (TOMS)
Positive stable block triangular preconditioners for symmetric saddle point problems
Applied Numerical Mathematics
Journal of Computational Physics
Constraint Schur complement preconditioners for nonsymmetric saddle point problems
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Applied Numerical Mathematics
New choices of preconditioning matrices for generalized inexact parameterized iterative methods
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations
Applied Numerical Mathematics
Stabilization and scalable block preconditioning for the Navier-Stokes equations
Journal of Computational Physics
Constraint preconditioners for solving singular saddle point problems
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Semi-convergence analysis of Uzawa methods for singular saddle point problems
Journal of Computational and Applied Mathematics
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We introduce a preconditioner for the linearized Navier--Stokes equations that is effective when either the discretization mesh size or the viscosity approaches zero. For constant coefficient problems with periodic boundary conditions, we show that the preconditioning yields a system with a single eigenvalue equal to 1, so that performance is independent of both viscosity and mesh size. For other boundary conditions, we demonstrate empirically that convergence depends only mildly on these parameters and we give a partial analysis of this phenomenon. We also show that some expensive subsidiary computations required by the new method can be replaced by inexpensive approximate versions of these tasks based on iteration, with virtually no degradation of performance.