Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
MSP: A Class of Parallel Multistep Successive Sparse Approximate Inverse Preconditioning Strategies
SIAM Journal on Scientific Computing
Factorized Sparse Approximate Inverses for Preconditioning
The Journal of Supercomputing
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
Sparse Approximate Inverses and Target Matrices
SIAM Journal on Scientific Computing
A massively parallel exponential integrator for advection-diffusion models
Journal of Computational and Applied Mathematics
An efficient parallel implementation of the MSPAI preconditioner
Parallel Computing
A Block FSAI-ILU Parallel Preconditioner for Symmetric Positive Definite Linear Systems
SIAM Journal on Scientific Computing
Parallel inexact constraint preconditioners for saddle point problems
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part II
Parallel acceleration of krylov solvers by factorized approximate inverse preconditioners
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
Adaptive Pattern Research for Block FSAI Preconditioning
SIAM Journal on Scientific Computing
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In this paper we propose a parallel preconditioner for the CG solver based on successive applications of the FSAI preconditioner. We first compute an FSAI factor G out for coefficient matrix A, and then another FSAI preconditioner is computed for either the preconditioned matrix $S = G_{\rm out} A G_{\rm out}^T$ or a sparse approximation of S. This process can be iterated to obtain a sequence of triangular factors whose product forms the final preconditioner. Numerical results onto large SPD matrices arising from geomechanical models account for the efficiency of the proposed preconditioner which provides a reduction of the iteration number and of the CPU time of the iterative phase with respect to the original FSAI preconditioner. The proposed preconditioner reveals particularly efficient for accelerating an iterative procedure to find the smallest eigenvalues of SPD matrices, where the increased setup cost of the RFSAI preconditioner does not affect the overall performance, being a small percentage of the total CPU time.