Parallel algorithms for indefinite linear systems
Parallel Computing - Parallel matrix algorithms and applications
A High Performance Algorithm for Incompressible Flows Using Local Solenoidal Functions
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Proceedings of the 18th annual international conference on Supercomputing
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
Original article: Aperiodic, chaotic lid-driven square cavity flows
Mathematics and Computers in Simulation
On HSS-based constraint preconditioners for generalized saddle-point problems
Numerical Algorithms
A-posteriori error analysis to the exterior Stokes problem
Applied Numerical Mathematics
Semi-convergence analysis of Uzawa methods for singular saddle point problems
Journal of Computational and Applied Mathematics
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The generalized Stokes problem, which arises frequently in the simulation of time-dependent Navier--Stokes equations for incompressible fluid flow, gives rise to symmetric linear systems of equations. These systems are indefinite due to a set of linear constraints on the velocity, causing difficulty for most preconditioners and iterative methods. This paper presents a novel method to obtain a preconditioned linear system from the original one which is then solved by an iterative method. This new method generates a basis for the velocity space and solves a reduced system which is symmetric and positive definite. Numerical experiments indicating superior convergence compared to existing methods are presented. A natural extension of this method to elliptic problems is also proposed, along with theoretical bounds on the rate of convergence, and results of experiments demonstrating robust and effective preconditioning.