Distributed Block Independent Set Algorithms and Parallel Multilevel ILU Preconditioners

We present a class of parallel preconditioning strategies utilizing multilevel block incomplete LU (ILU) factorization techniques to solve large sparse linear systems. The preconditioners are constructed by exploiting the concept of block independent sets. Two algorithms for constructing block independent sets of a sparse matrix in a distributed environment are proposed. We compare a few implementations of the parallel multilevel ILU preconditioners with different block independent set construction strategies and different Schur complement preconditioning strategies. We also use some diagonal thresholding and perturbation strategies for the block independent set construction and for the last level Schur complement ILU factorization. Numerical experiments indicate that our domain based parallel multilevel block ILU preconditioners are robust and efficient