Adjoint computations by algorithmic differentiation of a parallel solver for time-dependent PDEs

José I. Cardesa (1) , Laurent Hascoët (2) , Christophe Airiau (1)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 Ecuador - Transformations et outils informatiques pour le calcul scientifique

A computational fluid dynamics code is differentiated using algorithmic differentiation (AD) in both tangent and adjoint modes. The two novelties of the present approach are (1) the adjoint code is obtained by letting the AD tool Tapenade invert the complete layer of message passing interface (MPI) communications, and (2) the adjoint code integrates time-dependent, non-linear and dissipative (hence physically irreversible) PDEs with an explicit time integration loop running for ca. 106 time steps. The approach relies on using the Adjoinable MPI library to reverse the non-blocking communication patterns in the original code, and by controlling the memory overhead induced by the time-stepping loop with binomial checkpointing. A description of the necessary code modifications is provided along with the validation of the computed derivatives and a performance comparison of the tangent and adjoint codes.

Mots clés: Algorithmic differentiation; Computational fluid dynamics; Sensitivity analysis; Adjoint methods; Parallel computing

Domaines: Mécanique des fluides [physics.class-ph]

José I. Cardesa, Laurent Hascoët, Christophe Airiau. Adjoint computations by algorithmic differentiation of a parallel solver for time-dependent PDEs. Journal of computational science, 2020, 45, pp.101155. ⟨10.1016/j.jocs.2020.101155⟩. ⟨hal-03033123⟩