Block-implicit multigrid solution of Navier-Stokes equations in primitive variables
Journal of Computational Physics
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A preconditioned iterative method for saddlepoint problems
SIAM Journal on Matrix Analysis and Applications
Analysis and convergence of the MAC scheme. I: The linear problem
SIAM Journal on Numerical Analysis
Fast iterative solution of stabilised Stokes systems, part I: using simple diagonal preconditioners
SIAM Journal on Numerical Analysis
Inexact and preconditioned Uzawa algorithms for saddle point problems
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Downwind numbering: robust multigrid for convection—diffusion problems
Applied Numerical Mathematics - Special issue on multilevel methods
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
Efficient preconditioning of the linearized Navier—Stokes equations for incompressible flow
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
High order accurate solution of the incompressible Navier-Stokes equations
Journal of Computational Physics
Preconditioning Strategies for Models of Incompressible Flow
Journal of Scientific Computing
FGMRES preconditioning by symmetric/skew-symmetric decomposition of generalized stokes problems
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Application of modified homotopy perturbation method for solving the augmented systems
Journal of Computational and Applied Mathematics
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations
Applied Numerical Mathematics
Modified homotopy perturbation method for solving the Stokes equations
Computers & Mathematics with Applications
On HSS-based constraint preconditioners for generalized saddle-point problems
Numerical Algorithms
Efficient Preconditioners for Optimality Systems Arising in Connection with Inverse Problems
SIAM Journal on Control and Optimization
On generalized parameterized inexact Uzawa method for a block two-by-two linear system
Journal of Computational and Applied Mathematics
A preconditioned GLHSS iteration method for non-Hermitian singular saddle point problems
Computers & Mathematics with Applications
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Discretization and linearization of the incompressible Navier-Stokes equations leads to linear algebraic systems in which the coefficient matrix has the form of a saddle point problem (F B BT O) (u p) = (f g). In this paper, we describe the development of efficient and general iterative solution algorithms for this class of problems. We review the case where (1) arises from the steady-state Stokes equations and show that solution methods such as the Uzawa algorithm lead naturally to a focus on the Schur complement operator BF-1BT together with efficient strategies of applying the action of F-1 to a vector. We then discuss the advantages of explicitly working with the coupled form of the block system (1). Using this point of view, we describe some new algorithms derived by developing efficient methods for the Schur complement systems arising from the Navier-Stokes equations, and we demonstrate their effectiveness for solving both steady-state and evolutionary problems.