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We study algorithmic approaches for recovering from the failure of severalcompute nodes in the parallel preconditioned conjugate gradient (PCG) solver onlarge-scale parallel computers. In particular, we analyze and extend an exactstate reconstruction (ESR) approach, which is based on a method proposed byChen (2011). In the ESR approach, the solver keeps redundant information fromprevious search directions, so that the solver state can be fully reconstructedif a node fails unexpectedly. ESR does not require checkpointing or externalstorage for saving dynamic solver data and has low overhead compared to thefailure-free situation.  In this paper, we improve the fault tolerance of the PCG algorithm based onthe ESR approach. In particular, we support recovery from simultaneous oroverlapping failures of several nodes for general sparsity patterns of thesystem matrix, which cannot be handled by Chen's method. For this purpose, werefine the strategy for how to store redundant information across nodes. Weanalyze and implement our new method and perform numerical experiments withlarge sparse matrices from real-world applications on 128 nodes of the ViennaScientific Cluster (VSC). For recovering from three simultaneous node failureswe observe average runtime overheads between only 2.8% and 55.0%. The overheadof the improved resilience depends on the sparsity pattern of the systemmatrix.

How to Make the Preconditioned Conjugate Gradient Method Resilient Against Multiple Node Failures