MultiStage Approaches for Optimal Offline Checkpointing

Abstract

The computation of derivatives for optimizing time-dependent flow problems is often based on the integration of the adjoint differential equation. For this purpose, the knowledge of the complete forward solution is required. In the area of flow control, especially for three-dimensional problems, it may be impossible to keep track of the full forward solution due to the lack of storage capacities. One usual method to overcome this problem is checkpointing. Using a checkpointing strategy, only parts of the forward solution are kept in the main memory and additional time steps have to be performed. If one extends this approach such that some checkpoints can be stored on disc too, one can reduce the number of additional time steps. On the other hand, one has to take the access cost to one checkpoint into account. On parallel machines, one may use parallel I/O facilities to store and retrieve checkpoints. In these cases, the access cost of the checkpoints is also no longer negligible. Therefore, in this paper, the write and read counts for each checkpoint in a binomial checkpointing approach are examined. This way, the overall access cost to checkpoints is minimized. Numerical results illustrate the derived checkpointing approaches. They also show that checkpointing techniques may reduce the overall computing time despite the required recalculations.