Incremental Incomplete Lu Factorizations with Applications to Time-dependent Pdes

This paper addresses the problem of computing preconditioners for solving linear systems of equations with a sequence of slowly varying matrices. This problem arises in many important applications. For example, a common situation in computational fluid dynamics, is when the equations change only slightly, possibly in some parts of the physical domain. In such situations it is wastful to recompute entirely any LU or ILU factorizations computed for the previous coefficient matrix. This papers examines a number of techniques for computing incremental ILU factorizations. For example we consider techniques based on approximate inverses as well as alternating techniques for updating the factors L and U of the factorization.