A Bit-Compatible Shared Memory Parallelization for ILU(k) Preconditioning and a Bit-Compatible Generalization to Distributed Memory

ILU(k) is an important preconditioner widely used in many linear algebra solvers for sparse matrices. Unfortunately, there is still no highly scalable parallel ILU(k) algorithm. This paper presents the first such scalable algorithm. For example, the new algorithm achieves 50 times speedup with 80 nodes for general sparse matrices of dimension 160,000 that are diagonally dominant. The algorithm assumes that each node has sufficient memory to hold the matrix. The parallelism is task-oriented. We present experimental results for k = 1 and k = 2, which are the most commonly used cases in the practical applications. The results are presented for three platforms: a departmental cluster with Gigabit Ethernet; a high-performance cluster using an InfiniBand interconnect; and a simulation of a Grid computation with two or three participating sites.