Self-stabilizing fine-grained parallel incomplete LU factorization

This paper presents an investigation into the use of various mechanisms for improving the resilience of the fine-grained parallel algorithm for computing an incomplete LU factorization. These include various approaches to checkpointing as well as a study into the feasibility of using a self-stabilizing periodic correction step. Results concerning convergence of all of the self-stabilizing variants of the algorithm with respect to the occurrence of faults, and the impact of any sub-optimality in the produced incomplete L and U factors in Krylov subspace solvers are given. Numerical tests show that the simple algorithmic changes suggested here can ensure convergence of the fine-grained parallel incomplete factorization, and improve the performance of the resulting factors as preconditioners in Krylov subspace solvers in the presence of transient soft faults.