An hybrid direct-iterative solver based on a hierarchical interface decomposition

Parallel sparse direct solvers are now able to solve efficiently real-life three-dimensional problems having in the order of several millions of equations. They are, however, constrained by prohibitive memory requirements. Iterative methods on the other hand require much less memory, but they often fail to solve ill-conditioned systems. We propose an hybrid direct-iterative method which aims at bridging the gap between these two classes of method. In recent years, a few Incomplete LU factorization techniques were developed with the goal of combining some of the features of standard ILU preconditioners with the good scalability features of multi-level methods. The key feature of these techniques is to reorder the system in order to extract parallelism in a natural way. Often a number of ideas from domain decomposition are utilized and combined to derive parallel factorizations [1, 2, 3]. We propose an approach which is in this category.