Fault-tolerant linear solvers via selective reliability
  Energy increasingly constrains modern computer hardware, yet protecting computations and data against errors costs energy. This holds at all scales, but especially for the largest parallel computers being built and planned today. As processor counts continue to grow, the cost of ensuring reliability consistently throughout an application will become unbearable. However, many algorithms only need reliability for certain data and phases of computation. This suggests an algorithm and system codesign approach. We show that if the system lets applications apply reliability selectively, we can develop algorithms that compute the right answer despite faults. These "fault-tolerant" iterative methods either converge eventually, at a rate that degrades gracefully with increased fault rate, or return a clear failure indication in the rare case that they cannot converge. Furthermore, they store most of their data unreliably, and spend most of their time in unreliable mode.   We demonstrate this for the specific case of detected but uncorrectable memory faults, which we argue are representative of all kinds of faults. We developed a cross-layer application / operating system framework that intercepts and reports uncorrectable memory faults to the application, rather than killing the application, as current operating systems do. The application in turn can mark memory allocations as subject to such faults. Using this framework, we wrote a fault-tolerant iterative linear solver using components from the Trilinos solvers library. Our solver exploits hybrid parallelism (MPI and threads). It performs just as well as other solvers if no faults occur, and converges where other solvers do not in the presence of faults. We show convergence results for representative test problems. Near-term future work will include performance tests. 
Patrick G. Bridges, Kurt B. Ferreira, Michael A. Heroux, Mark Hoemmen
math.NA cs.DC cs.PF