We introduce block versions of the multi-elimination incomplete LU (ILUM) factorization preconditioning technique for solving general sparse unstructured linear systems. These preconditioners have a multi-level structure and exhibit properties that are typically enjoyed by multigrid methods. Several heuristic strategies for forming blocks of independent set are introduced and their relative merits are discussed. Advantages of block ILUM over point ILUM include increased robustness and efficiency. We compare several versions of the block ILUM, point ILUM and the dual-thresholdbased ILUT preconditioners. In particular, the ILUM preconditioned Krylov subspace solver is tested for some convection-diffusion problems to show convergence that is near Reynolds number independent and near grid independent.
|
742
|
Iterative Methods for Sparse Linear Systems
– Saad
- 2003
|
|
438
|
Direct Methods for Sparse Matrices
– Erisman, Reid
- 1990
|
|
396
|
Computer Solution of Large Sparse Positive Definite Systems
– George, Liu
- 1981
|
|
268
|
Sparse matrix test problems
– DUFF, GRIMES, et al.
- 1989
|
|
240
|
Users’ guide for the Harwell-Boeing sparse matrix collection (release I
– Duff, Grimes, et al.
- 1992
|
|
199
|
der Vorst. An iterative solution method for linear systems of which the coe cient matrix is a symmetric M-matrix
– Meijerink, van
- 1977
|
|
182
|
A flexible inner-outer preconditioned GMRES algorithm
– Saad
- 1993
|
|
73
|
Block preconditioning for the conjugate gradient method
– Concus, Golub, et al.
- 1985
|
|
69
|
The multifrontal solution of unsymmetric sets of linear equations
– Duff, Reid
- 1984
|
|
63
|
Krylov subspace methods on supercomputers
– Saad
|
|
55
|
Direct methods for solving symmetric indefinite systems of linear equations
– Bunch, Parlett
- 1971
|
|
51
|
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
– Saad
- 1996
|
|
50
|
Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems
– D'Azevedo, Forsyth, et al.
- 1992
|
|
50
|
A single cell high order scheme for the convection-diffusion equation with variable coefficients, Int
– Gupta, Manohar, et al.
- 1984
|
|
47
|
Experimental study of ILU preconditioners for indefinite matrices
– Chow, Saad
- 1997
|
|
43
|
GMRES: A Generalized Minimal Residual Method for solving nonsymmetric linear systems
– Saad, Schultz
- 1986
|
|
39
|
de Zeeuw. Matrix–dependent prolongations and restrictions in a blackbox multigrid solver
– M
- 1990
|
|
35
|
Towards a cost-effective ILU preconditioner with high level fill
– D’Azevedo, Forsyth, et al.
- 1992
|
|
29
|
Solving sparse triangular systems on parallel computers
– Anderson, Saad
- 1988
|
|
29
|
Fourier analysis of a robust multigrid method for convectiondiffusion equations
– Reusken
- 1995
|
|
25
|
High-order ilu preconditioners for cfd problems
– CHAPMAN, SAAD
|
|
25
|
On convergence and performance of iterative methods with fourth-order compact schemes
– Zhang
- 1998
|
|
24
|
Multilevel ILU decomposition
– Bank, Wagner
- 1999
|
|
23
|
A parallel hybrid sparse linear system solver
– Gallivan, Sameh, et al.
- 1990
|
|
23
|
Highly parallel preconditioners for general sparse matrices
– Saad
|
|
21
|
Polynomial preconditionings for conjugate gradient calculations
– Johnson, Micchelli, et al.
- 1983
|
|
21
|
Algebraic multilevel iteration method for Stieltjes matrices
– Axelsson, Neytcheva
- 1994
|
|
20
|
Ordering techniques for the preconditioned conjugate gradient method on parallel computers
– Elman, Agron
- 1989
|
|
20
|
Domain decomposition and multi-level type techniques for general sparse linear systems
– Saad, Sosonkina, et al.
- 1998
|
|
19
|
A compact multigrid solver for convection-diffusion equations
– Gupta, Kouatchou, et al.
- 1997
|
|
19
|
Direct Methods for Sparse Matrices
– Osterby, Zlatev
|
|
18
|
Application of sparse matrix solvers as effective preconditioners
– Young, Melvin, et al.
- 1989
|
|
17
|
Use of iterative refinement in the solution of sparse linear systems
– Zlatev
- 1982
|
|
16
|
Diagonal threshold techniques in robust multi-level ILU preconditioners for general sparse linear systems
– Saad, Zhang
- 1999
|
|
15
|
A survey of multilevel preconditioned iterative methods. BIT
– Axelsson, Vassilevski
- 1989
|
|
14
|
Meurant, The effect of reordering on preconditioned conjugate gradients
– Duff, A
- 1989
|
|
14
|
Approximate cyclic reduction preconditioning
– Reusken
- 1997
|
|
13
|
ILUT: a dual threshold incomplete ILU preconditioner
– Saad
- 1994
|
|
12
|
On approximate factorization methods for block-matrices suitable for vector and parallel
– Axelsson, Polman
- 1986
|
|
10
|
Accelerated multigrid high accuracy solution of the convection-diffusion equation with high Reynolds number
– Zhang
- 1997
|
|
9
|
Wubs, A fast linear-system solver for large unstructured problems on a shared-memory computer
– Botta, Ploeg, et al.
- 1996
|
|
9
|
MRILU: it's the preconditioning that counts
– Botta, Wubs
- 1997
|
|
9
|
The effect of reordering on the preconditioned GMRES algorithm for solving the compressible Navier-Stokes equations
– Dutto
- 1993
|
|
9
|
MRILU: an effective algebraic multi-level ILU-preconditioner for sparse matrices
– Botta, Wubs
- 1999
|
|
7
|
Incomplete block-matrix factorization iterative methods for convection-diffusion problems
– Axelsson, Eijkhout, et al.
- 1989
|
|
7
|
Independent set orderings for parallel matrix factorizations by Gaussian elimination
– Leuze
- 1989
|
|
7
|
On convergence of iterative methods for a fourth-order discretization scheme
– Zhang
|
|
6
|
der Vorst. A vectorizable version of some ICCG methods
– van
- 1982
|
|
6
|
guide for the Harwell-Boeing sparse matrix collection (Release 1
– Users’
- 1992
|
|
3
|
a multi-elimination ILU preconditioner for general sparse matrices
– ILUM
- 1996
|
|
