Standard preconditioning techniques based on incomplete LU (ILU) factorizations offer a limited degree of parallelism, in general. A few of the alternatives advocated so far consist of either using some form of polynomial preconditioning, or applying the usual ILU factorization to a matrix obtained from a multicolor ordering. In this paper we present an incomplete factorization technique based ...

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...

In this work, we develop a fast hierarchical solver for solving large, sparse least squares problems. We build upon the algorithm, spaQR (sparsified QR Gnanasekaran and Darve in SIAM J Matrix Anal Appl 43(1):94–123, 2022), that was developed by authors to solve large linear systems. Our algorithm is built on top of Nested Dissection based multifrontal approach. use low-rank approximations front...

A dual reordering strategy based on both threshold and graph reorderings is introduced to construct robust incomplete LU (ILU) factorization of indefinite matrices. The ILU matrix is constructed as a preconditioner for the original matrix to be used in a preconditioned iterative scheme. The matrix is first divided into two parts according to a threshold parameter to control diagonal dominance. ...

This paper presents a new fine-grained parallel algorithm for computing an incomplete LU factorization. All nonzeros in the incomplete factors can be computed in parallel and asynchronously, using one or more sweeps that iteratively improve the accuracy of the factorization. Unlike existing parallel algorithms, the new algorithm does not depend on reordering the matrix. Numerical tests show tha...

We present an incomplete UL IUL decomposition of matrixAwhich is extracted as a by-product of BFAPINV backward factored approximate inverse process. We term this IUL factorization as IULBF. We have used ILUFF 3 and IULBF as left preconditioner for linear systems. Different versions of ILUFF and IULBF preconditioners are computed by using different dropping techniques. In this paper, we compare ...

SUMMARY We describe a novel technique for computing a sparse incomplete factorization of a general symmetric positive deenite matrix A. The factorization is not based on the Cholesky algorithm (or Gaussian elimination), but on A{orthogonalization. Thus, the incomplete factorization always exists and can be computed without any diagonal modiication. When used in conjunction with the conjugate gr...

We propose an incomplete multifrontal LU-factorization (IMF) preconditioner that extends supernodal multifrontal methods to incomplete factorizations. It can be used as a preconditioner in a Krylov-subspace method to solve large-scale sparse linear systems with an element structure; e.g., those arising from a finite element discretization of a partial differential equation. The fact that the el...

A method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix A is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations. It is proved that in exact arithmetic the preconditioner is well defined if A is an H-matrix. The results of numerical experiments are pre...

Incomplete factorization preconditioners based on recursive red–black orderings have been shown efficient for discrete second order elliptic PDEs with isotropic coefficients. However, they suffer for some weakness in presence of anisotropy or grid stretching. Here we propose to combine these orderings with block incomplete factorization preconditioning techniques. For implementation considerati...