This paper introduces several strategies to deal with pivot blocks in multi-level block incomplete LU factorization (BILUM) preconditioning techniques. These techniques are aimed at increasing the robustness and controlling the amount of fill-ins of BILUM for solving large sparse linear systems when large-size blocks are used to form block-independent set. Techniques proposed in this paper include double-dropping strategies, approximate singular-value decomposition, variable size blocks and use of an arrowhead block submatrix. We point out the advantages and disadvantages of these strategies and discuss their efficient implementations. Numerical experiments are conducted to show the usefulness of the new techniques in dealing with hard-to-solve problems arising from computational fluid dynamics. In addition, we discuss the relation between multi-level ILU preconditioning methods and algebraic multi-level methods.
- Algebraic multigrid method
- Incomplete LU factorization
- Krylov subspace methods
- Multi-elimination ILU factorization
- Multi-level ILU preconditioner