Algebraic multilevel preconditioning methods, II
SIAM Journal on Numerical Analysis
The nested recursive two-level factorization method for nine-point difference matrices
SIAM Journal on Scientific and Statistical Computing
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
Iterative solution methods
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 sparsity patterns for the inverse of a matrix and preconditioning
IMACS'97 Proceedings on the on Iterative methods and preconditioners
SIAM Journal on Scientific Computing
Matrix Renumbering ILU: An Effective Algebraic Multilevel ILU Preconditioner for Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Sparse Approximate Inverse Smoother for Multigrid
SIAM Journal on Matrix Analysis and Applications
Algebraic Multilevel Methods and Sparse Approximate Inverses
SIAM Journal on Matrix Analysis and Applications
Multilevel ILU With Reorderings for Diagonal Dominance
SIAM Journal on Scientific Computing
Preconditioning of Boundary Value Problems Using Elementwise Schur Complements
SIAM Journal on Matrix Analysis and Applications
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In this work we analyse a method to construct numerically efficient and computationally cheap sparse approximations of some of the matrix blocks arising in the block-factorized preconditioners for matrices with a two-by-two block structure. The matrices arise from finite element discretizations of partial differential equations. We consider scalar elliptic problems, however the approach is appropriate also for other types of problems such as parabolic problems or systems of equations. The technique is applicable for both selfadjoint and non-selfadjoint problems, in two as well as in three space dimensions. We analyse in detail the two-dimensional case and provide extensive numerical evidence for the efficiency of the proposed matrix approximations, both serial and parallel. Two- and three-dimensional tests are included.