ILUT: A dual threshold incomplete LU factorization

In this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends the usual ILU(0) factorization without using the concept of level of ll-in. There are two traditional ways of developing incomplete factorization preconditioners. The rst uses a symbolic factorization approach in which a level of ll is attributed to each ll-in element using only the graph of the matrix. Then each ll-in that is introduced is dropped whenever its level of ll exceeds a certain threshold. The second class of methods consists of techniques derived from modiications of a given direct solver by including a drop-oo rule, based on the numerical size of the ll-ins introduced. traditionally referred to as threshold preconditioners. The rst type of approach may not be reliable for indeenite problems, since it does not consider numerical values. The second is often far more expensive than the standard ILU(0). The strategy we propose is a compromise between these two extremes.