Direct methods for sparse matrices
Direct methods for sparse matrices
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
On finding supernodes for sparse matrix computations
SIAM Journal on Matrix Analysis and Applications
A framework for block ILU factorizations using block-size reduction
Mathematics of Computation
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Parallel threshold-based ILU factorization
SC '97 Proceedings of the 1997 ACM/IEEE conference on Supercomputing
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
A Scalable Parallel Algorithm for Incomplete Factor Preconditioning
SIAM Journal on Scientific Computing
PASTIX: a high-performance parallel direct solver for sparse symmetric positive definite systems
Parallel Computing - Parallel matrix algorithms and applications
Recent Progress in General Sparse Direct Solvers
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Adapting a parallel sparse direct solver to architectures with clusters of SMPs
Parallel Computing - Special issue: Parallel and distributed scientific and engineering computing
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
PT-Scotch: A tool for efficient parallel graph ordering
Parallel Computing
Tunable Parallel Experiments in a GridRPC Framework: Application to Linear Solvers
High Performance Computing for Computational Science - VECPAR 2008
Journal of Computational Physics
A Supernodal Approach to Incomplete LU Factorization with Partial Pivoting
ACM Transactions on Mathematical Software (TOMS)
Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning
SIAM Journal on Scientific Computing
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Among existing preconditioners, the level-of-fill ILU has been quite popular as a general-purpose technique. Experimental observations have shown that, when coupled with block techniques, these methods can be quite effective in solving realistic problems arising from various applications. In this work, we consider an extension of this kind of method which is suitable for parallel environments. Our method is developed from the framework of high performance sparse direct solvers. The main idea we propose is to define an adaptive blockwise incomplete factorization that is much more accurate (and numerically more robust) than the scalar incomplete factorizations commonly used to precondition iterative solvers. These requirements lead to a robust class of parallel preconditioners based on generalized versions of block ILU techniques.