This paper tests a number of ILU-type preconditioners for solving indeenite linear systems which arise from complex applications such as Computational Fluid Dynamics. Both point and block preconditioners are considered. The paper focuses on ILU factorization which can be computed with high accuracy by allowing liberal amounts of ll-in. A number of strategies for enhancing the stability of the f...

A graph theoretic process that models level-based, incomplete LU factorization (ILU(`)) of sparse unsymmetric matrices is developed. The model leads to two incomplete fill path theorems that are generalizations of the original fill path theorem of Rose, Tarjan, and Lueker. Our S-level incomplete fill path theorem leads to the development of new, embarrassingly parallel algorithms for computing ...

A Newton–Krylov method is developed for the solution of the steady compressible Navier– Stokes equations using a discontinuous Galerkin (DG) discretization on unstructured meshes. Steady-state solutions are obtained using a Newton–Krylov approach where the linear system at each iteration is solved using a restarted GMRES algorithm. Several different preconditioners are examined to achieve fast ...

We discuss issues related to domain decomposition and multilevel preconditioning techniques which are often employed for solving large sparse linear systems in parallel computations. We introduce a class of parallel preconditioning techniques for general sparse linear systems based on a two level block ILU factorization strategy. We give some new data structures and strategies to construct loca...

Incomplete factorization preconditioners such as ILU, ILUT and MILU are well-known robust general-purpose techniques for solving linear systems on serial computers. However, they are difficult to parallelize efficiently. Various techniques have been used to parallelize these preconditioners, such as multicolor orderings and subdomain preconditioning. These techniques may degrade the performance...

Standard preconditioning techniques based on incomplete LU (ILU) factorizations offer a limited degree of parallelism, in general. A few of the alternatives advocated so far consist of either using some form of polynomial preconditioning, or applying the usual ILU factorization to a matrix obtained from a multicolor ordering. In this paper we present an incomplete factorization technique based ...

We design a grid based multilevel incomplete LU preconditioner (GILUM) for solving general sparse matrices. This preconditioner combines a high accuracy ILU factorization with an algebraic multilevel recursive reduction. The GILUM precondi-tioner is a compliment to the domain based multilevel block ILUT preconditioner. A major diierence between these two preconditioners is the way that the coar...

A Newton-Krylov method is developed for the solution of the steady compressible Navier-Stokes equations using a Discontinuous Galerkin (DG) discretization on unstructured meshes. An element Line-Jacobi preconditioner is presented which solves a block tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (Block-ILU(0)) is also presented as a precond...

A recently proposed Minimum Discarded Fill (MDF ) ordering (or pivoting) technique is e ective in nding high quality ILU (`) preconditioners, especially for problems arising from unstructured nite element grids. This algorithm can identify anisotropy in complicated physical structures and orders the unknowns in a \preferred" direction. However, the MDF ordering is costly, when ` increases. In t...