A Multilevel Dual Reordering Strategy for Robust Incomplete LU Factorization of Indefinite Matrices

@article{Zhang2001AMD,
  title={A Multilevel Dual Reordering Strategy for Robust Incomplete LU Factorization of Indefinite Matrices},
  author={Jun Zhang},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2001},
  volume={22},
  pages={925-947}
}
  • Jun Zhang
  • Published 1 June 2000
  • Computer Science
  • SIAM J. Matrix Anal. Appl.
A dual reordering strategy based on both threshold and graph reorderings is introduced to construct robust incomplete LU (ILU) factorization of indefinite matrices. The ILU matrix is constructed as a preconditioner for the original matrix to be used in a preconditioned iterative scheme. The matrix is first divided into two parts according to a threshold parameter to control diagonal dominance. The first part with large diagonal dominance is reordered using a graph-based strategy, followed by an… 
Hybrid reordering strategies for ILU preconditioning of indefinite sparse matrices
TLDR
This work presents hybrid reordering strategies to deal with incomplete LU factorization preconditioning techniques, which include new diagonal reorderings that are in conjunction with a symmetric nondecreasing degree algorithm.
Distributed block independent set algorithms and parallel multilevel ILU preconditioners
Incomplete factorization by local exact factorization (ILUE)
HILUCSI: Simple, robust, and fast multilevel ILU for large‐scale saddle‐point problems from PDEs
TLDR
To enable superior efficiency for large‐scale systems with millions or more unknowns, HILUCSI introduces a scalability‐oriented dropping in conjunction with a variant of inverse‐based dropping, and it is shown that this combination improves robustness for indefinite systems without compromising efficiency.
A two-phase preconditioning strategy of sparse approximate inverse for indefinite matrices
Scalable Task-Oriented Parallelism for Structure Based Incomplete LU Factorization
TLDR
This paper presents the first highly scalable parallelILU(k) algorithm, which achieves 50 times speedup with 80 nodes for general sparse matrices of dimension 160,000 that are diagonally dominant.
HILUCSI: Simple, Robust, and Fast Multilevel ILU with Mixed Symmetric and Unsymmetric Processing
TLDR
The robustness and efficiency of HILUCSI are demonstrated for benchmark problems from a wide range of applications against ILUPACK, the supernodal ILUTP in SuperLU, and multithreaded direct solvers in PARDISO and MUMPS.
Parallel Multilevel Sparse Approximate Inverse Preconditioners in Large Sparse Matrix Computations
TLDR
The use of the multistep successive preconditioning strategies (MSP) to construct a class of parallel multilevel sparse approximate inverse (SAI) preconditionsers is investigated to enhance the robustness of SAI for solving difficult problems.
Parallel multilevel block ILU preconditioning techniques for large sparse linear systems
We present a class of parallel preconditioning strategies built on a multilevel block incomplete LU (ILU)factorization technique to solve large sparse linear systems on distributed memory parallel
...
...

References

SHOWING 1-10 OF 68 REFERENCES
BILUTM: A Domain-Based Multilevel Block ILUT Preconditioner for General Sparse Matrices
TLDR
This implementation is efficient in controlling the fill-in elements during the multilevel block ILU factorization, especially when large size blocks are used in domain decomposition-type implementations.
ILUM: A Multi-Elimination ILU Preconditioner for General Sparse Matrices
  • Y. Saad
  • Computer Science
    SIAM J. Sci. Comput.
  • 1996
TLDR
The ILUM factorization described in this paper can be viewed as a multifrontal version of a Gaussian elimination procedure with threshold dropping which has a high degree of potential parallelism.
Diagonal threshold techniques in robust multi-level ILU preconditioners for general sparse linear systems
TLDR
Techniques based on diagonal threshold tolerance when developing multi-elimination and multi-level incomplete LU (ILUM) factorization precondi-tioners for solving general sparse linear systems are introduced.
An Assessment of Incomplete-LU Preconditioners for Nonsymmetric Linear Systems
TLDR
A direct method is currently more appropriate than an iterative method for a general-purpose black-box nonsymmetric linear solver and pivoting is even more important for incomplete than for complete factorizations.
On the stability of the incomplete LU-factorizations and characterizations of H-matrices
Summary. Meijerink and van der Vorst [8] have shown that the incomplete LU-factorizations are numerically stable for M-matrices. Varga, Saff and Mehrmann [16] gave some characterizations of the
Comparative Analysis of the Cuthill–McKee and the Reverse Cuthill–McKee Ordering Algorithms for Sparse Matrices
TLDR
It is proved that for band elimination methods, the two orderings are equivalent and that, surprisingly, the reverse ordering is always at least as good as the original one when envelope elimination techniques are used.
SOR as a preconditioner
...
...