Scalable and Fault Tolerant Computation with the Sparse Grid Combination Technique

摘要

This paper continues to develop a fault tolerant extension of the sparse gridcombination technique recently proposed in [B. Harding and M. Hegland, ANZIAMJ., 54 (CTAC2012), pp. C394-C411]. The approach is novel for two reasons, firstit provides several levels in which one can exploit parallelism leading towardsmassively parallel implementations, and second, it provides algorithm-basedfault tolerance so that solutions can still be recovered if failures occurduring computation. We present a generalisation of the combination techniquefrom which the fault tolerant algorithm is a consequence. Using a model for thetime between faults on each node of a high performance computer we providebounds on the expected error for interpolation with this algorithm. Numericalexperiments on the scalar advection PDE demonstrate that the algorithm isresilient to faults on a real application. It is observed that the trade-off ofrecovery time to decreased accuracy of the solution is suitably small. Acomparison with traditional checkpoint-restart methods applied to thecombination technique show that our approach is highly scalable with respect tothe number of faults.