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...

ILU smoothers are good smoothers for linear multigrid methods. In this paper, a new ILU smoother for the incompressible Navier-Stokes equations, called CILU (Collective ILU), is designed, based on r-transformations. Existing ILU decompositions factorize the matrix with real elements. In CILU the elements of the matrix that is factorized are submatrices, corresponding to the set of physical vari...

A dual reordering strategy based on both threshold and graph reorderings is introduced to construct robust incomplete LU (ILU) factorization of indefinite matrices. The ILU matrix is constructed as a preconditioner for the original matrix to be used in a preconditioned iterative scheme. The matrix is first divided into two parts according to a threshold parameter to control diagonal dominance. ...

ILU(k) is a commonly used preconditioner for iterative linear solvers for sparse, non-symmetric systems. It is often preferred for the sake of its stability. We present TPILU(k), the first efficiently parallelized ILU(k) preconditioner that maintains this important stability property. Even better, TPILU(k) preconditioning produces an answer that is bit-compatible with the sequential ILU(k) prec...

We present a class of parallel preconditioning strategies utilizing multilevel block incomplete LU (ILU) factorization techniques to solve large sparse linear systems. The preconditioners are constructed by exploiting the concept of block independent sets (BISs). Two algorithms for constructing BISs of a sparse matrix in a distributed environment are proposed. We compare a few implementations o...

We present a class of parallel preconditioning strategies built on a multilevel block incomplete LU (ILU) factorization technique to solve large sparse linear systems on distributed memory parallel computers. The preconditioners are constructed by using the concept of block independent sets. Two algorithms for constructing block independent sets of a distributed sparse matrix are proposed. We c...

A multi-level preconditioned iterative method based on a multi-level block ILU factoriza-tion preconditioning technique is introduced and is applied to the solution of unstructured sparse linear systems arising from the numerical simulation of coating problems. The coef-cient matrices usually have several rows with zero diagonal values that may cause stability diiculty in standard ILU factoriza...