Towards a Cost-effective Ilu Preconditioner with Higher Level Fills

A recently proposed Minimum Discarded Fill (MDF ) ordering (or pivoting) technique is e ective in nding high quality ILU (`) preconditioners, especially for problems arising from unstructured nite element grids. This algorithm can identify anisotropy in complicated physical structures and orders the unknowns in a \preferred" direction. However, the MDF ordering is costly, when ` increases. In this paper, several less expensive variants of the MDF technique are explored to produce coste ective ILU preconditioners. The Incomplete MDF and Threshold MDF orderings combine MDF ideas with drop tolerance techniques to identify the sparsity pattern in the ILU preconditioners. These techniques produce orderings that encourage fast decay of the entries in the ILU factorization. The Minimum Update Matrix (MUM ) ordering technique is a simpli cation of the MDF ordering and is an analogue of the minimum degree algorithm. The MUM ordering is especially e ective for large matrices arising from Navier-Stokes problems.