Fault tolerant variants of the fine-grained parallel incomplete LU factorization

This paper presents an investigation into fault tolerance for the fine-grained parallel algorithm for computing an incomplete LU factorization. Results concerning the convergence of the algorithm with respect to the occurrence of faults, and the impact of any sub-optimality in the produced incomplete 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 use of the resulting factors as preconditioners in Krylov subspace solvers if faults do occur.