A stability analysis of incomplete LU factorizations
Mathematics of Computation
Approximate Schur complement reconditioners on serial and parallel computers
SIAM Journal on Scientific and Statistical Computing
Nested grids ILU-decomposition (NGILU)
Proceedings of the 6th international congress on Computational and applied mathematics
On the algebraic multigrid method
Journal of Computational Physics
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
SIAM Journal on Scientific Computing
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Approximate Inverse Techniques for Block-Partitioned Matrices
SIAM Journal on Scientific Computing
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Scalable Parallel Preconditioning with the Sparse Approximate Inverse of Triangular Matrices
SIAM Journal on Matrix Analysis and Applications
BILUTM: A Domain-Based Multilevel Block ILUT Preconditioner for General Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Applied Numerical Mathematics
Enhanced multi-level block ILU preconditioning strategies for general sparse linear systems
Journal of Computational and Applied Mathematics
Applied Mathematics and Computation
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Parallel Multilevel Sparse Approximate Inverse Preconditioners in Large Sparse Matrix Computations
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
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We investigate the use of sparse approximate inverse techniques (SAI) in a grid based multilevel ILU preconditioner (GILUM) to design a robust and parallelizable preconditioner for solving general sparse matrices. Taking the advantages of grid based multilevel methods, the resulting preconditioner outperforms sparse approximate inverse in robustness and efficiency. Conversely, taking the advantages of sparse approximate inverse, it affords an easy and convenient way to introduce parallelism within multilevel structure. Moreover, an independent set search strategy with automatic diagonal thresholding and a relative threshold dropping strategy are proposed to improve preconditioner performance. Numerical experiments are used to show the effectiveness and efficiency of the proposed preconditioner, and to compare it with some single and multilevel preconditioners.