Fault-tolerant finite-element multigrid algorithms with hierarchically compressed asynchronous checkpointing

• Fault-tolerant and robust multigrid methods.
• Hierarchical finite element compression.
• Asynchronous checkpointing with local restart.

We analyse novel fault tolerance schemes for data loss in multigrid solvers, which essentially combine ideas of checkpoint-restart with algorithm-based fault tolerance. To improve efficiency compared to conventional global checkpointing, we exploit the inherent data compression of the multigrid hierarchy, and relax the synchronicity requirement through a local failure local recovery approach. We experimentally identify the root cause of convergence degradation in the presence of data loss using smoothness considerations. Our resulting schemes form a family of techniques that can be tailored to the expected error probability of (future) large-scale machines. A performance model gives further insight into the benefits and applicability of our techniques.