Approximate Inverse Techniques for Block-Partitioned Matrices

Authors:
Edmond Chow;Yousef Saad
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1997

Citing 0
Cited 13

An object-oriented framework for block preconditioning

ACM Transactions on Mathematical Software (TOMS)
Preconditioning techniques for large linear systems: a survey

Journal of Computational Physics
Multigrid treatment and robustness enhancement for factored sparse approximate inverse preconditioning

Applied Numerical Mathematics
A parallel block multi-level preconditioner for the 3D incompressible Navier--Stokes equations

Journal of Computational Physics
Some greedy learning algorithms for sparse regression and classification with mercer kernels

The Journal of Machine Learning Research
Multilevel block ILU preconditioner for sparse nonsymmetric M-matrices

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations

Journal of Computational Physics
FGMRES preconditioning by symmetric/skew-symmetric decomposition of generalized stokes problems

Mathematics and Computers in Simulation
On some new approximate factorization methods for block tridiagonal matrices suitable for vector and parallel processors

Mathematics and Computers in Simulation
Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning

SIAM Journal on Scientific Computing
Finite-element based sparse approximate inverses for block-factorized preconditioners

Advances in Computational Mathematics
Schur Complement Preconditioners for Surface Integral-Equation Formulations of Dielectric Problems Solved with the Multilevel Fast Multipole Algorithm

SIAM Journal on Scientific Computing
VBARMS: A variable block algebraic recursive multilevel solver for sparse linear systems

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.02

Visualization

Abstract

This paper proposes some preconditioning options when the system matrix is in block-partitioned form. This form may arise naturally, for example, from the incompressible Navier--Stokes equations, or may be imposed after a domain decomposition reordering. Approximate inverse techniques are used to generate sparse approximate solutions whenever these are needed in forming the preconditioner. The storage requirements for these preconditioners may be much less than for incomplete LU factorization (ILU) preconditioners for tough, large-scale computational fluid dynamics (CFD) problems. The numerical experiments show that these preconditioners can help solve difficult linear systems whose coefficient matrices are highly indefinite.