In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo [7]. Numerical results for a variety of finite element discretizations of both steady and unsteady incompre...

In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo in [8]. Numerical results for a variety of finite element discretizations of both steady and unsteady incom...

In this paper, we study a composite preconditioner that combines the modified tangential frequency filtering decomposition with the ILU(0) factorization. Spectral property of the composite preconditioner is examined by the approach of Fourier analysis. We illustrate that condition number of the preconditioned matrix by the composite preconditioner is asymptotically bounded by O(h − 2 3 p ) on a...

This paper presents a robust structured multifrontal factorization method for large symmetric positive definite sparse matrices arising from the discretization of partial differential equations (PDEs). For PDEs such as 2D and 3D elliptic equations, the method costs roughly O(n) and O(n4/3) flops, respectively. The algorithm takes advantage of a low-rank property in the direct factorization of s...

For unsymmetric block-tridiagonal systems of linear equations arising from the discretization of partial differential equations, a composite preconditioner is proposed and tested. It combines a classical ILU0 factorization for high frequencies with a tangential filtering preconditioner. The choice of the filtering vector is important: the test-vector is the Ritz eigenvector corresponding to the...

Abstract. This paper analyzes the cache efficiency of two high-performance sparse Cholesky factorization algorithms: the multifrontal algorithm and the left-looking algorithm. These two are essentially the only two algorithms that are used in current codes; generalizations of these algorithms are used in general-symmetric and general-unsymmetric sparse triangular factorization codes. Our theore...

The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to block linear systems arising from three-field displacement-velocity-pressure formulation of coupled poromechanics. For its application, however, it necessary invert blocks with algebraic form C ˆ = ( + ? F T ) , where symmetric positive definite matrix, rank-deficient ...

A preconditioned scheme for solving sparse symmetric eigenproblems is proposed. The solution strategy relies upon the DACG algorithm, which is a Preconditioned Conjugate Gradient algorithm for minimizing the Rayleigh Quotient. A comparison with the well established ARPACK code, shows that when a small number of the leftmost eigenpairs is to be computed, DACG is more efficient than ARPACK. Effec...