A multilevel Crout ILU preconditioner with pivoting and row permutation

In this paper, we present a new incomplete LU factorization using pivoting by columns and row permutation. Pivoting by columns helps to avoid small pivots and row permutation is used to promote sparsity. This factorization is used in a multilevel framework as a preconditioner for iterative methods for solving sparse linear systems. In most multilevel incomplete ILU factorization preconditioners, preprocessing (scaling and permutation of rows and columns of the coefficient matrix) results in further improvements. Numerical results illustrate that these preconditioners are suitable for a wide variety of applications.