Matrix renumbering ILU: An effective algebraic multilevel ILU preconditioner for sparse matrices

In this paper a multilevel-like ILU preconditioner is introduced. The ILU factorization generates its own ordering during the elimination process. Both ordering and dropping depend on the size of the entries. The method can handle structured and unstructured problems. Results are presented for some important classes of matrices and for several well-known test examples. The results illustrate the effciency of the method and show in several cases near grid independent convergence