Sensitivity analysis for mixed-language numerical models

The separation of concerns in the development of numerical models not only leads to a separation into components but, based on their purpose, these components may also be written in different programming languages. The sensitivity analysis of a numerical model provides quantitative information about the dependencies of the model outputs with respect to its inputs. An analysis of mixed-language models using derivatives computed with algorithmic (or automatic) differentiation needs to comprehensively handle all the involved components and the respective interfaces in a mixed-language environment. We describe the issues arising in the context of the sensitivity analysis, present a solution implemented with the algorithmic differentiation tool Rapsodia for C++ and Fortran, and discuss its practical use in a large-scale engineering application.