FT-GCR：一个容错的广义共轭剩余椭圆解算器
FT-GCR: a fault-tolerant generalized conjugate residual elliptic solver
摘要：
随着以越来越小的硬件组件为特征的高性能计算系统的稳步发展，用于数值模拟的系统和算法越来越多地与由硬件故障和计算数据的比特级错误表示引起的中断相抗衡。在利用大规模处理能力的数值框架中，线性系的解通常代表计算最密集的部分。由于涉及大量的重复操作，迭代求解器特别容易受到位翻转的影响。提出了一种新的方法FT-GCR，它为预处理的广义共轭残差Krylov求解器提供了软故障的检测和恢复。该算法测试的单调递减的剩余范数，失败时，重新开始迭代的局部Krylov空间内。数值实验所产生的一个椭圆形问题的解决方案，从一个孤立的山丘上的球体上的静止流显示的技能的方法，在解决位翻转的范围内的网格大小和数据丢失的情况下，获得最佳的回报和检测率较大的腐败事件。该方法的简单性使得它很容易扩展到其他求解器和集成模型弹性策略内的算法容错的理想候选者。
英文摘要：
With the steady advance of high performance computing systems featuring smaller and smaller hardware components, the systems and algorithms used for numerical simulations increasingly contend with disruptions caused by hardware failures and bit-levels misrepresentations of computing data. In numerical frameworks exploiting massive processing power, the solution of linear systems often represents the most computationally intensive component. Given the large amount of repeated operations involved, iterative solvers are particularly vulnerable to bit-flips. A new method named FT-GCR is proposed here that supplies the preconditioned Generalized Conjugate Residual Krylov solver with detection of, and recovery from, soft faults. The algorithm tests on the monotonic decrease of the residual norm and, upon failure, restarts the iteration within the local Krylov space. Numerical experiments on the solution of an elliptic problem arising from a stationary flow over an isolated hill on the sphere show the skill of the method in addressing bit-flips on a range of grid sizes and data loss scenarios, with best returns and detection rates obtained for larger corruption events. The simplicity of the method makes it easily extendable to other solvers and an ideal candidate for algorithmic fault tolerance within integrated model resilience strategies.
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