How fast are nonsymmetric matrix iterations
SIAM Journal on Matrix Analysis and Applications
Iterative solution methods
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
BILUTM: A Domain-Based Multilevel Block ILUT Preconditioner for General Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
High accuracy multigrid solution of the 3D convection-diffusion equation
Applied Mathematics and Computation
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
Algebraic Multilevel Methods and Sparse Approximate Inverses
SIAM Journal on Matrix Analysis and Applications
A Multilevel Dual Reordering Strategy for Robust Incomplete LU Factorization of Indefinite Matrices
SIAM Journal on Matrix Analysis and Applications
MSP: A Class of Parallel Multistep Successive Sparse Approximate Inverse Preconditioning Strategies
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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We investigate the use of the multistep successive preconditioning strategies (MSP) to construct a class of parallel multilevel sparse approximate inverse (SAI) preconditioners. We do not use independent set ordering, but a diagonal dominance based matrix permutation to build a multilevel structure. The purpose of introducing multilevel structure into SAI is to enhance the robustness of SAI for solving difficult problems. Forward and backward preconditioning iteration and two Schur complement preconditioning strategies are proposed to improve the performance and to reduce the storage cost of the multilevel preconditioners. One version of the parallel multilevel SAI preconditioner based on the MSP strategy is implemented. Numerical experiments for solving a few sparse matrices on a distributed memory parallel computer are reported.