GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity
SIAM Journal on Scientific Computing
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Preconditioners for saddle point problems arising in computational fluid dynamics
Applied Numerical Mathematics
A Preconditioner for Generalized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
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
An Efficient Solver for the Incompressible Navier-Stokes Equations in Rotation Form
SIAM Journal on Scientific Computing
Pressure Schur Complement Preconditioners for the Discrete Oseen Problem
SIAM Journal on Scientific Computing
A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations
Journal of Computational Physics
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In this paper we introduce a new preconditioner for linear systems of saddle point type arising from the numerical solution of the Navier-Stokes equations. Our approach is based on a dimensional splitting of the problem along the components of the velocity field, resulting in a convergent fixed-point iteration. The basic iteration is accelerated by a Krylov subspace method like restarted GMRES. The corresponding preconditioner requires at each iteration the solution of a set of discrete scalar elliptic equations, one for each component of the velocity field. Numerical experiments illustrating the convergence behavior for different finite element discretizations of Stokes and Oseen problems are included.