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This paper presents a new fine-grained parallel algorithm for computing an incomplete LU factorization. All nonzeros in the incomplete factors can be computed in parallel and asynchronously, using one or more sweeps that iteratively improve the accuracy of the factorization. Unlike existing parallel algorithms, the amount of parallelism is large irrespective of the ordering of the matrix, and matrix ordering can be used to enhance the accuracy of the factorization rather than to increase parallelism. Numerical tests show that very few sweeps are needed to construct a factorization that is an effective preconditioner.
Chow et al. (Thu,) studied this question.