An optimal memory-reduced procedure for calculating adjoints of the instationary Navier–Stokes equations

This paper discusses approximation schemes for adjoints in control of the instationary Navier–Stokes system. It tackles the storage problem arising in the numerical calculation of the appearing adjoint equations by proposing a low-storage approach which utilizes optimal checkpointing. For this purpose, a new proof of optimality is given. This new approach gives so far unknown properties of the optimal checkpointing strategies and thus provides new insights. The optimal checkpointing allows a remarkable memory reduction by accepting a slight increase in run-time caused by repeated forward integrations as illustrated by means of the Navier–Stokes equations. In particular, a memory reduction of two orders of magnitude causes only a slow down factor of 2–3 in run-time.