In this paper we analyze a preconditioner for mixed finite element systems arising in the approximation of a second order lliptic problem with Neumann boundary conditions by triangular non-conforming elements. This problem stems from the so called rojection methods for the unsteady Navier–Stokes equations and is one of the most computationally intensive parts of the method. he present study is ...

This paper analyzes dropping strategies in a multilevel incomplete LU decomposition context and presents a few of strategies for obtaining related ILUs with enhanced robustness. The analysis shows that the Incomplete LU factorization resulting from dropping small entries in Gaussian elimination produces a good preconditioner when the inverses of these factors have norms that are not too large. ...

We consider symmetric preconditioning strategies for the iterative solution of dense complex symmetric non-Hermitian systems arising in computational electromagnetics. In particular we report on the numerical behaviour of the classical Incomplete Cholesky factorization as well as some of its recent variants and consider also well known factorized approximate inverses. We illustrate the difficul...

This paper presents an investigation into fault tolerance for the fine-grained parallel algorithm for computing an incomplete LU factorization. Results concerning the convergence of the algorithm with respect to the occurrence of faults, and the impact of any sub-optimality in the produced incomplete factors in Krylov subspace solvers are given. Numerical tests show that the simple algorithmic ...

In this article the notions of semi weak orthogonality and semi weak factorization structure in a category $mathcal X$ are introduced. Then the relationship between semi weak factorization structures and quasi right (left) and weak factorization structures is given. The main result is a characterization of semi weak orthogonality, factorization of morphisms, and semi weak factorization structur...

Incomplete Cholesky factorizations have long been important as preconditioners for use in solving largescale symmetric positive-definite linear systems. In this paper, we focus on the relationship between two important positive semidefinite modification schemes that were introduced to avoid factorization breakdown, namely the approach of Jennings and Malik and that of Tismenetsky. We present a ...

The Crout variant of ILU preconditioner (ILUC) developed recently has been shown to have a number of advantages over ILUT, the conventional row-based ILU preconditioner [14]. This paper explores pivoting strategies for sparse symmetric matrices to improve the robustness of ILUC. This paper shows how to integrate two symmetry-preserving pivoting strategies, the diagonal pivoting and the Bunch-Ka...

Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential equations derived by considering the mass conservation of each phase (e.g., oil, water), along with constitutive laws for the relationship of phase velocity to ...

Incomplete Cholesky factorisation based preconditioners have been widely used in association with the Conjugate Gradient Method. The standard incomplete Cholesky factorisation, or IC(0) factorisation, forces the Cholesky factor L (where A LL T) to have the same sparsity as A. Two main strategies exist for controlling the amount of ll; namely control based upon position (or ll level) and control...

In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new matrix format suitable for GPU devices. Parallel lower triangular solvers and upper triangular solvers are developed for this new data structure. With these solv...