Online Checkpointing for Parallel Adjoint Computation in PDEs: Application to Goal-Oriented Adaptivity and Flow Control

摘要

The computation of derivatives for the optimization of time-dependent flow problems is based on the integration of the adjoint differential equation. For this purpose, the knowledge of the complete forward solution is required. Similar information is needed for a posteriori error estimation with respect to a given functional. In the area of flow control, especially for three dimensional problems, it is usually impossible to store the full forward solution due to the lack of memory capacities. Additionally, adaptive time-stepping procedures are needed for efficient integration schemes in time. Therefore, standard optimal offline checkpointing strategies are usually not well-suited in that framework. We present a new online procedure for determining the checkpoint distribution on the fly. Complexity estimates and consequences for storing and retrieving the checkpoints using parallel I/O are discussed. The resulting checkpointing approach is integrated in HiFlow, a multipurpose parallel finite-element package with a strong emphasis in computational fluid dynamic, reactive flows and related subjects. Using an adjoint-based error control for prototypical three dimensional flow problems, numerical experiments demonstrate the effectiveness of the proposed approach.