A preconditioned iterative method for saddlepoint problems
SIAM Journal on Matrix Analysis and Applications
Fast iterative solution of stabilised Stokes systems, part I: using simple diagonal preconditioners
SIAM Journal on Numerical Analysis
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Iterative solution methods
Efficient iterative methods for Saddle Point problems
Efficient iterative methods for Saddle Point problems
An Efficient Iterative Method for the Generalized Stokes Problem
SIAM Journal on Scientific Computing
Parallel Simulation of Particulate Flows
IRREGULAR '98 Proceedings of the 5th International Symposium on Solving Irregularly Structured Problems in Parallel
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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Saddle-point problems give rise to indefinite linear systems that are challenging to solve via iterative methods. This paper surveys two recent techniques for solving such problems arising in computational fluid dynamics. The systems are indefinite due to linear constraints imposed on the fluid velocity. The first approach, known as the multilevel algorithm, employs a hierarchical technique to compute the constrained linear space for the unknowns, followed by the iterative solution of a positive definite reduced problem. The second approach exploits the banded structure of sparse matrices to obtain a different reduced system which is determined by the unknowns common to adjacent block rows. Although the reduced system in this approach may still be indefinite, the algorithm converges to the solution at an accelerated rate. These methods have two desirable characteristics, namely, robust numerical convergence and efficient parallelizability. The paper presents the performance of these methods for incompressible particulate flow problems on a shared-memory parallel architecture.