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...

Conjugate gradient (CG) methods to solve sparse systems of linear equations play an important role in numerical methods for solving discretized partial diierential equations. The large size and the condition of many technical or physical applications in this area result in the need for eecient par-allelization and preconditioning techniques of the CG method. In particular for very ill-condition...

In this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends the usual ILU(0) factorization without using the concept of level of ll-in. There are two traditional ways of developing incomplete factorization preconditioners. The rst uses a symbolic factorization approach in which a level of ll is attributed ...

The paper analyses various parallel incomplete factorizations based on the non-overlapping domain decomposition. The general framework is applied to the investigation of the preconditioning step in cg-like methods. Under certain conditions imposed on the nite element mesh, all matrix and vector types given by the special data distribution can be used in the matrix-by-vector multiplications. Not...

Motivated by the numerical solution of the linearized incompressible Navier–Stokes equations, we study threshold incomplete LU factorizations for non-symmetric saddle point matrices. The resulting preconditioners are used to accelerate the convergence of a Krylov subspace method applied to finite element discretizations of fluid dynamics problems in three space dimensions. The paper presents an...

This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in main memory (RAM), and must instead be stored on slow external devices such as disks (out-of-core or out-of-memory). Traditional (such the column pivoted QR factorization singular value decomposition) very communication intensive they require many vector-vector matrix-v...

We describe the iterative solution of dense linear systems arising from a surface integral equation of electromagnetic scattering. The complex symmetric version of QMR has been used as an iterative solver together with a sparse approximate inverse preconditioner. The preconditioner is computed using the topological information from the computational mesh. The matrix-vector products are computed...

In this paper an approach for finding a sparse incomplete Cholesky factor through an incomplete orthogonal factorization with Givens rotations is discussed and applied to Gaussian Markov random fields (GMRFs). The incomplete Cholesky factor obtained from the incomplete orthogonal factorization is usually sparser than the commonly used Cholesky factor obtained through the standard Cholesky facto...

| It is well known that ordering of unknowns greatly a ects convergence in Incomplete LU (ILU) factorization preconditioned iterative methods. The authors recently proposed a simple evaluation way for orderings in ILU preconditioning. The evaluation index, which has a simple relationship with a norm of a remainder matrix, is easily computed without additional memory requirement. The computation...

Motivated by the numerical solution of the linearized incompressible Navier–Stokes equations, we study threshold incomplete LU factorizations for nonsymmetric saddle-point matrices. The resulting preconditioners are used to accelerate the convergence of a Krylov subspace method applied to finite element discretizations of fluid dynamics problems in three space dimensions. The paper presents and...