Abstract

Gradient-based optimization for large-scale problems governed by unsteady PDEs, in which gradients with respect to the design variables are computed using unsteady adjoint, are characterized by the backward in time integration of the adjoint equations, which require the instantaneous primal/flow fields to be available at each time-step. The most widely used technique to reduce storage requirements, at the expense of a controlled number of recomputations, is binomial check-pointing. Alternatively, one may profit of lossless and lossy compression techniques, such as iPGDZ+, this paper relies upon. iPGDZ+is a hybrid algorithm which consists of (a) an incremental variant of the Proper Generalized Decomposition (iPGD), (b) the ZFP and (c) the Zlib compression algorithms. Two different implementations of iPGDZ+are described: (a) the Compressed Full Storage (CFS ) strategy which stores the whole time-history of the flow solution using iPGDZ+and (b) the Compressed Coarse-grained Check-Pointing (3CP ) technique which combines iPGDZ+with check-pointing. Assessment in aerodynamic shape optimization problems in terms of storage saving, computational cost and representation accuracy are included along with comparisons with binomial check-pointing. The methods presented are implemented within the in-house version of the publicly available adjointOptimisation library of OpenFOAM, for solving the flow and adjoint equations and conducting the optimization.