Solving sparse triangular linear systems on parallel computers
International Journal of High Speed Computing
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
Scalable iterative solution of sparse linear systems
Parallel Computing
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Parallel programming with MPI
Parallel Preconditioning with Sparse Approximate Inverses
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
Approximate sparsity patterns for the inverse of a matrix and preconditioning
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Efficient parallel computation of ILU(k) preconditioners
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Incomplete Cholesky Factorizations with Limited Memory
SIAM Journal on Scientific Computing
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
A parallel solver for large-scale Markov chains
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
Crout Versions of ILU for General Sparse Matrices
SIAM Journal on Scientific Computing
An MPI Implementation of the SPAI Preconditioner on the T3E
International Journal of High Performance Computing Applications
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
A comparison of projective and direct solvers for finite elements in elastostatics
Advances in Engineering Software
Adaptive Pattern Research for Block FSAI Preconditioning
SIAM Journal on Scientific Computing
Banded target matrices and recursive FSAI for parallel preconditioning
Numerical Algorithms
A generalized Block FSAI preconditioner for nonsymmetric linear systems
Journal of Computational and Applied Mathematics
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A novel parallel preconditioner for symmetric positive definite matrices is developed coupling a generalized factored sparse approximate inverse (FSAI) with an incomplete LU (ILU) factorization. The generalized FSAI, called block FSAI, is derived by requiring the preconditioned matrix to resemble a block-diagonal matrix in the sense of the minimal Frobenius norm. An incomplete block Jacobi algorithm is then effectively used to accelerate the convergence of a Krylov subspace method. The block FSAI-ILU preconditioner proves superior to both FSAI and the incomplete block Jacobi by themselves in a number of realistic finite element test cases and is fully scalable for a given number of blocks.