Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1016/S0167-8191(01)00140-5 | Parallel Computing |
Keywords | Field | DocType |
parallel algorithm,linear constraint,computational fluid dynamics,iterative methods,fluid velocity,algorithm converges,indefinite linear system,different reduced system,computa- tional fluid dynamics,parallel computing,reduced system,iterative method,saddle-point problems,preconditioning,computational fluid dynamic,linear space,positive definite reduced problem,parallel computer,shared memory,positive definite,linear system,iteration method,fluid dynamics,band structure,sparse matrices | Convergence (routing),Applied mathematics,Mathematical optimization,Linear system,Iterative method,Parallel algorithm,Computer science,Parallel computing,Linear space,Positive-definite matrix,Computational fluid dynamics,Sparse matrix | Journal |
Volume | Issue | ISSN |
28 | 2 | Parallel Computing |
Citations | PageRank | References |
2 | 0.38 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ahmed H. Sameh | 1 | 297 | 139.93 |
| Vivek Sarin | 2 | 102 | 19.50 |