BILUM: Block versions of multielimination and multilevel ILU preconditioner for general sparse linear systems

We introduce block versions of the multielimination incomplete LU (ILUM) fa ctorization preconditioning technique for solving general sparse unstructur ed linear systems. These preconditioners have a multilevel structure and, f or certain types of problems, may exhibit properties that are typically enj oyed by multigrid methods. Several heuristic strategies for forming blocks of independent sets are introduced and their relative merits are discussed. The advantages of block ILUM over point ILUM include increased robustness and efficiency. We compare several versions of the block ILUM, point ILUM, and the dual-threshold-based ILUT preconditioners. In particular, tests wit h some convection-diffusion problems show that it may be possible to obtain convergence that is nearly independent of the Reynolds number as well as o f the grid size.