Low-overhead fault-tolerance for the preconditioned conjugate gradient solver

Linear system solvers are an integral part for many different compute-intensive applications and they benefit from the compute power of heterogeneous computer architectures. However, the growing spectrum of reliability threats for such nano-scaled CMOS devices makes the integration of fault tolerance mandatory. The preconditioned conjugate gradient (PCG) method is one widely used solver as it finds solutions typically faster compared to direct methods. Although this iterative approach is able to tolerate certain errors, latest research shows that the PCG solver is still vulnerable to transient effects. Even single errors, for instance, caused by marginal hardware, harsh environments, or particle radiation, can considerably affect execution times, or lead to silent data corruption. In this work, a novel fault-tolerant PCG solver with extremely low runtime overhead is proposed. Since the error detection method does not involve expensive operations, it scales very well with increasing problem sizes. In case of errors, the method selects between three different correction methods according to the identified error. Experimental results show a runtime overhead for error detection ranging only from 0.04% to 1.70%.