Parallel sparse direct solvers are now able to solve efficiently real-life three-dimensional problems having in the order of several millions of equations. They are, however, constrained by prohibitive memory requirements. Iterative methods on the other hand require much less memory, but they often fail to solve ill-conditioned systems. We propose an hybrid direct-iterative method which aims at...

Incomplete LU factorization preconditioners have been surprisingly successful for many cases of general nonsymmetric and indeenite matrices. However, their failure rate is still too high for them to be useful as black-box library software for general matrices. Besides fatal breakdowns due to zero pivots, the major causes of failure are inaccuracy, and instability of the triangular solves. When ...

Iterative solvers for sparse linear systems often benefit from using preconditioners. While there are implementations for many iterative methods that leverage the computing power of accelerators, porting the latest developments in preconditioners to accelerators has been challenging. In this paper we develop a selfadaptive multi-elimination preconditioner for graphics processing units (GPUs). T...

In this paper we investigate the application of Krylov methods to compressible ows, and the e ect of implicit boundary conditions on the implicit solution of nonlinear problems. Two defect-correction procedures, namely, Approximate Factorization (AF) for structured grids, and ILU/GMRES for general grids are considered. Also, considered here, is Newton-Krylov matrix-free methods that we combine ...

(1) Background: Exploring the interactive relationship between intensive land use (ILU) and tourism industry development (TID) is of vital significance to promote high-quality sustainable urban economy. (2) Methods: This paper constructs an evaluation index system ILU TID, comprehensively measures coupling interaction TID in China’s 58 major tourist cities from 2004 2018 by using entropy weight...

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...

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...

PHIDAL (Parallel Hierarchical Interface Decomposition ALgorithm) is a parallel incomplete factorization method which exploits a hierarchical interface decomposition of the adjacency graph of the coefficient matrix. The idea of the decomposition is similar to that of the well-known wirebasket techniques used in domain decomposition. However, the method is devised for general, irregularly structu...