SIAM Journal on Scientific and Statistical Computing
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Generalized approximate inverse finite element matrix techniques
Neural, Parallel & Scientific Computations
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Iterative Solution Methods for Modeling Multiphase Flow in Porous Media Fully Implicitly
SIAM Journal on Scientific Computing
Parallel Approximate Finite Element Inverse Preconditioning on Distributed Systems
ISPDC '04 Proceedings of the Third International Symposium on Parallel and Distributed Computing/Third International Workshop on Algorithms, Models and Tools for Parallel Computing on Heterogeneous Networks
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
Low-rank update of preconditioners for the inexact Newton method with SPD Jacobian
Mathematical and Computer Modelling: An International Journal
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In this work, preconditioners for the iterative solution by Krylov methods of the linear systems arising at each Newton iteration are studied. The preconditioner is defined by means of a Broyden-type rank-one update of a given initial preconditioner, at each nonlinear iteration, as described in [5] where convergence properties of the scheme are theoretically proved. This acceleration is employed in the solution of the nonlinear system of algebraic equations arising from the finite element discretization of two-phase flow model in porous media. We report numerical results of the application of this approach when the initial preconditioner is chosen to be the incomplete LU decomposition of the Jacobian matrix at the initial nonlinear stage. It is shown that the proposed acceleration reduces the number of linear iterations needed to achieve convergence. Also, the cost of computing the preconditioner is reduced as this operation is made only once at the beginning of the Newton iteration.