A grid-based multilevel incomplete LU factorization preconditioning technique for general sparse matrices

We design a grid-based multilevel incomplete LU preconditioner (GILUM) for solving general sparse matrices. This preconditioner combines a high accuracy ILU factorization with an algebraic multilevel recursive reduction. The GILUM preconditioner is a compliment to the domain-based multilevel block ILUT preconditioner. A major difference between these two preconditioners is the way that the coarse level nodes are chosen. The approach of GILUM is analogous to that of algebraic multigrid method. The GILUM approach avoids some controversial issues in algebraic multigrid method such as how to construct the interlevel transfer operators and how to compute the coarse level operator. Numerical experiments are conducted to compare GILUM with other ILU preconditioners.