A Multi-Level Preconditioner with Applications
to the Numerical Simulation of Coating Problems

Yousef Saad
Department of Computer Science and Engineering
University of Minnesota
4-192 EE/CS Building, 200 Union Street S.E.
Minneapolis, MN 55455, USA


Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA


A multi-level preconditioned iterative method based on a multi-level block ILU factorization preconditioning technique is introduced and is applied to the solution of unstructured sparse linear systems arising from the numerical simulation of coating problems. The coefficient matrices usually have several rows with zero diagonal values that may cause stability difficulty in standard ILU factorization techniques. The new preconditioning strategy employs a diagonal threshold tolerance and a local reordering of individual blocks to increase robustness of the multi-level block ILU factorization process.

Key words: sparse matrices, multi-level preconditioner, ILU factorization.

This paper has been submitted for Iterative Methods in Scientific Computation II, D. R. Kincaid et al. (eds), Proceedings of the IMACS Austin Conference celerating the 75th birthday of Professor David M. Young, Jr.