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

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. Keywords: sparse matrices, multi-level preconditioning, ILU factorization 1 Introduction In this paper, a multi-level block incomplete LU (ILU) preconditioning technique is designed for solving unstructured sparse linear systems from the numerical simulation of coating problems. Coating is a delicate process of putting a layer of one liquid material (film) over another solid material unifo..