Fault-tolerant grid-based solvers: Combining concepts from sparse grids and MapReduce

J. W. Larson, M. Hegland, B. Harding, S. Roberts, L. Stals, A. P. Rendell, P. Strazdins, M. M. Ali, C. Kowitz, R. Nobes, J. Southern, N. Wilson, M. Li, Y. Oishi

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Abstract

A key issue confronting petascale and exascale computing is the growth in probability of soft and hard faults with increasing system size. A promising approach to this problem is the use of algorithms that are inherently fault tolerant. We introduce such an algorithm for the solution of partial differential equations, based on the sparse grid approach. Here, the solution of multiple component grids are efficiently combined to achieve a solution on a full grid. The technique also lends itself to a (modified) MapReduce framework on a cluster of processors, with the map stage corresponding to allocating each component grid for solution over a subset of the processors, and the reduce stage corresponding to their combination. We describe how the sparse grid combination method can be modified to robustly solve partial differential equations in the presence of faults. This is based on a modified combination formula that can accommodate the loss of one or two component grids. We also discuss accuracy issues associated with this formula. We give details of a prototype implementation within a MapReduce framework using the dynamic process features and asynchronous message passing facilities of MPI. Results on a two-dimensional advection problem show that the errors after the loss of one or two sub-grids are within a factor of 3 of the sparse grid solution in the presence of no faults. They also indicate that the sparse grid technique with four times the resolution has approximately the same error as a full grid, while requiring (for a sufficiently high resolution) much lower computation and memory requirements. We finally outline a MapReduce variant capable of responding to faults in ways other than re-scheduling of failed tasks. We discuss the likely software requirements for such a flexible MapReduce framework, the requirements it will impose on users' legacy codes, and the system's runtime behavior.

Original languageEnglish
Pages (from-to)130-139
Number of pages10
JournalProcedia Computer Science
Volume18
DOIs
Publication statusPublished - 1 Jan 2013
Externally publishedYes
Event13th Annual International Conference on Computational Science, ICCS 2013 - Barcelona, Spain
Duration: 5 Jun 20137 Jun 2013

Bibliographical note

(CC BY-NC-ND) Open Access article licensed under a Creative Commons Attribution Non-Commercial No Derivatives license, which permits others to distribute this work non-commercially, provided the original work is properly cited and the use is non-commercial. If you remix, transform, or build upon the material, you may not distribute the modified material.

Keywords

  • Fault-tolerance
  • MapReduce
  • Parallel computing
  • Partial differential equations
  • Sparse grids

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    Larson, J. W., Hegland, M., Harding, B., Roberts, S., Stals, L., Rendell, A. P., Strazdins, P., Ali, M. M., Kowitz, C., Nobes, R., Southern, J., Wilson, N., Li, M., & Oishi, Y. (2013). Fault-tolerant grid-based solvers: Combining concepts from sparse grids and MapReduce. Procedia Computer Science, 18, 130-139. https://doi.org/10.1016/j.procs.2013.05.176