In this paper, we have used a complete pivoting strategy to compute the left-looking version of RIF preconditioner. This pivoting is based on the complete pivoting strategy of the IJK version of Gaussian Elimination process. There is a parameter α to control the pivoting process. To study the effect of α on the quality of the left-looking version of RIF preconditioner with complete pivoting str...

We present a preconditioner for saddle point problems which is based on an approximation of an implicit representation of the inverse of the saddle point matrix. Whereas this preconditioner does not require an approximation to the Schur complement, its theoretical analysis yields some interesting relationship to some Schurcomplement-based preconditioners. Whereas the evaluation of this new prec...

An algebraic multilevel (ML) preconditioner is presented for the Helmholtz equation in heterogeneous media. It is based on a multilevel incomplete LDLT factorization and preserves the inherent (complex) symmetry of the Helmholtz equation. The ML preconditioner incorporates two key components for efficiency and numerical stability: symmetric maximum weight matchings and an inverse-based pivoting...

In this paper we propose a parallel implementation of the FSAI preconditioner to accelerate the PCG method in the solution of symmetric positive definite linear systems of very large size. This preconditioner is used as building block for the construction of an indefinite Inexact Constraint Preconditioner (ICP) for saddle point-type linear systems arising from Finite Element (FE) discretization...

An eecient parallelizable preconditioner for solving large-scale CFD problems is presented. It is adapted to coarse-grain parallelism and can be used for both shared and distributed-memory parallel computers. The proposed preconditioner consists of two independent approximations of the system matrix. The rst one is a block-diagonal, fully paralleliz-able approximation of the given system. The s...

Consider the linear system of equations of the form Ax = b where the coefficient matrix A ∈ Rn×n is nonsingular, large, sparse and nonsymmetric and also x, b ∈ R. We refer to this system as the original system. An explicit preconditioner M for this system is an approximation of matrix A−1. In [1], Lou presented the Backward Factored INVerse or BFINV algorithm which computes the inverse factoriz...

In this paper we propose and describe a parallel implementation of a block preconditioner for the solution of saddle point linear systems arising from Finite Element (FE) discretization of 3D coupled consolidationproblems. TheMixedConstraint Preconditioner developed in [L. Bergamaschi,M. Ferronato, G. Gambolati,Mixed constraint preconditioners for the solution to FE coupled consolidation equati...

In the setting of 3D local mesh refinement, we present the theoretical construction and the implementation aspects of the Bramble-Pasciak-Xu (BPX) preconditioner. The refinement under consideration is the 3D local redgreen refinement procedure introduced by Bornemann-Erdmann-Kornhuber (BEK). We outline how to construct the theoretical optimality of the BPX preconditioner in the setting of ellip...

The original TPABLO algorithms are a collection of algorithms which compute a symmetric permutation of a linear system such that the permuted system has a relatively full block diagonal with relatively large nonzero entries. This block diagonal can then be used as a preconditioner. We propose and analyze three extensions of this approach: we incorporate a nonsymmetric permutation to obtain a la...

This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the Schrödinger equation as examples. This approach transforms the dense system of the pseudospectral discretization approximately into a sparse system via an equivalent i...