Novel Expression-Template-Based Automatic Differentiation of Fortran Codes for Aerodynamic Optimization

Abstract

An elegant and robust approach for discrete adjoint-based automatic differentiation of the Fortran codes is proposed in this work. The technique aims at bridging the gap within the Fortran programming language that currently lacks certain metaprogramming paradigms that are readily available at compile time in C/C++ codes. More specifically, the present work uses an expression-based tape approach, which is the first-of-its-kind implementation in Fortran programming language, that can significantly reduce the memory footprint while improving the computational efficiency of the adjoint-based automatic differentiation (AD). The proposed expression-template-based approach is incorporated in our in-house AD toolbox, which currently is the only Fortran-based tool in the literature that uses a fixed-point-type operator-overloading adjoint sensitivity analysis. The improved version of the fast automatic differentiation using operator-overloading technique toolbox is then coupled with the in-house unstructured parallel compressible (UNPAC) flow solver for a robust design optimization framework (DOF), called UNPAC-DOF. The efficiency and robustness of the proposed technique and the resulting framework are tested for aerodynamic shape optimization problems applied to airfoil and wing geometries.