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...

This article studies the effect of discretization order on preconditioning and convergence of a high-order Newton–Krylov unstructured flow solver. The generalized minimal residual (GMRES) algorithm is used for inexactly solving the linear system arising from implicit time discretization of the governing equations. A first-order Jacobian is used as the preconditioning matrix. The complete lower–...

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...

For solving large sparse symmetric linear systems, arising from the discretization of elliptic problems, the preferred choice is the preconditioned conjugate gradient method. The convergence rate of this method mainly depends on the condition number of the preconditioner chosen. Using Fourier analysis the condition number estimate of common preconditioning techniques for two dimensional ellipti...

This study develops an OpenMP scheme to parallel the preconditioned conjugate gradient methods (PCG) in shared memory computers. The proposed method is simple and systematic, so a minor change in traditional PCG methods may produce effective parallelism. At first, the global stiffness matrix is renumbered in order to produce a parallel three-line form matrix, and a subroutine only needs to be c...

For block-tridiagonal linear system of equations, a variant of tangential filtering preconditioners is proposed in this paper. The new variant is based on a twisted block factorization along with certain filtering property. For practical usage, a class of composite preconditioners tested, which are constructed by combining the twisted tangential filtering decomposition preconditioner with the c...

The ILU-based preconditioning methods in previous work have their own parameters to improve their performances. Although the parameters may degrade the performance, their determination is left to users. Thus, these previous methods are not reliable in practical computer-aided engineering use. This paper proposes a novel ILU-based preconditioner called the auto-accelerated ILU, or AILU. In order...

The Legendre spectral Galerkin method of self-adjoint second order elliptic equations usually results in a linear system with dense and ill-conditioned coefficient matrix. In this paper, the is solved by preconditioned conjugate gradient (PCG) where preconditioner M constructed approximating variable coefficients (T+1)-term series each direction to desired accuracy. A feature proposed PCG that ...

Multiscale methods have been developed to solve multiphase flow and transport problems in large-scale heterogeneous porous media accurately and efficiently. In this report, the computational efficiency of the multiscale finite-volume method (MSFV) is analyzed. The power of MSFV lies in its ability to combine local basis functions with a global coarse-scale problem to solve highly details hetero...