Multi-level ILU-factorizations for eigenvalue computation and continuation

In recent years substantial progress has been made in the development of multi-level ILU-factorizations. In some cases, current versions already show (near) grid-independent convergence and therefore are attractive for very large problems. In this paper a variant called MRILU is described and applied in a continuation code. Furthermore, it is shown how such an accurate factorization can be used as approximate Jacobian in an eigenvalue solver. MRILU can handle both scalar equations and systems of partial differential equations.