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 employe...

We consider parallel preconditioning schemes to accelerate the convergence of Conjugate Gradients (CG) for sparse linear system solution. We develop methods for constructing and applying preconditioners on multiprocessors using incomplete factorizations with selective inversion for improved latency-tolerance. We provide empirical results on the efficiency, scalability and quality of our precond...

In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems. In earlier works, the local Schur complements were computed exactly using a sparse direct solver. The robustness of the preconditioner comes at the price of this memory and time intensive computation that is th...

Incomplete LU factorization is a valuable preconditioning approach for sparse iterative solvers. An “ideal” but inefficient preconditioner for the iterative solution of Ax = b is A−1 itself. This paper describes a preconditioner based on sparse approximations to partitioned representations of A−1, in addition to the results of implementation of the proposed method in a shared memory parallel en...

We present a class of parallel preconditioning strategies utilizing multilevel block incomplete LU (ILU) factorization techniques to solve large sparse linear systems. The preconditioners are constructed by exploiting the concept of block independent sets (BISs). Two algorithms for constructing BISs of a sparse matrix in a distributed environment are proposed. We compare a few implementations o...

We study two implementation strategies to utilize Schur complement technique in multilevel recursive incomplete LU preconditioning techniques (RILUM) for solving general sparse matrices. The first strategy constructs a RILUM to precondition the original matrix. The second strategy solves the first Schur complement matrix using the lower level parts of the RILUM as the preconditioner. We discuss...

We present two new ways of preconditioning sequences of nonsymmetric linear systems in the special case where the implementation is matrix-free. Both approaches are fully algebraic, they are based on the general updates of incomplete LU decompositions recently introduced in [1], and they may be directly embedded into nonlinear algebraic solvers. The first of the approaches uses a new model of p...

To date, the most efficient solver used in the weather sciences for the resolution of linear system in numerical weather prediction is the generalized minimal residual method called GMRES. However, difficulties still appear in matrix resolution when the GMRES iterative method is used without an appropriate preconditioner. For improving the computation speed in numerically solving weather equati...

A version of the Bi-CGSTAB method is applied for solving the linear systems that typically occur when applying the Newton method to a discretized set of coupled elliptic partial di erential equations in two dimensions. The Incomplete Line LU decomposition is generalized for the case of coupled equations and applied as a preconditioner. A suitable stopping criterion is developed for the Bi-CGSTA...

The Crout variant of ILU preconditioner (ILUC) developed recently has been shown to have a number of advantages over ILUT, the conventional row-based ILU preconditioner [14]. This paper explores pivoting strategies for sparse symmetric matrices to improve the robustness of ILUC. This paper shows how to integrate two symmetry-preserving pivoting strategies, the diagonal pivoting and the Bunch-Ka...