Reducing memory requirements of unsteady adjoint by synergistically using check‐pointing and compression.

The unsteady adjoint method used in gradient‐based optimization in 2D and, particularly, 3D industrial problems modeled by unsteady PDEs may have significant storage requirements and/or computational cost. The reason for this is that the backward in time integration of the adjoint equations requires the previously computed instantaneous flow fields to be available at each time‐step. This article proposes remedies to this problem, by extending/upgrading relevant techniques proposed by the group of authors as well as other researchers. Their applicability is wide, even if these remedies are herein demonstrated in shape optimization problems in unsteady fluid mechanics. Check‐pointing is in widespread use as it reduces the memory footprint and CPU cost of the optimization with a controllable computational overhead. Alternatively, flow field time‐series can be stored in a lossless or lossly compressed form. The novelty of this article is the development of a Compressed Coarse‐grained Check‐Pointing strategy for second‐order accurate schemes in time, by optimally combining check‐pointing and lossy compression. The latter includes (a) the incremental Proper Generalized Decomposition (iPGD) algorithm and (b) a hybridization of the iPGD with the ZFP and Zlib algorithms. This is implemented within OpenFOAM, which is used to solve the flow and adjoint equations and conduct the optimization, and assessed in 2D/3D aerodynamic shape optimization problems on unstructured grids. Effectiveness in data reduction, computational cost, and reconstruction accuracy are compared, vis‐à‐vis also to the "standard" binomial check‐pointing technique after adjusting it to second‐order accurate schemes in time. [ABSTRACT FROM AUTHOR]