Computational Differentiation and Multidisciplinary Design

Multidisciplinary Design Optimization (MDO) by means of formal sensitivity analysis requires that each single-discipline analysis code supply not only the output functions for the (usually constrained) optimization process and other discipline analysis inputs, but also the derivatives of all of these output functions with respect to its input variables. Computational differentiation techniques and automatic aifferentiation tools enable MDO by providing accurate and efficient derivatives of computer programs with little human effort. We discuss the principles behind automatic differentiation and give a brief overview of automatic differentiation tools and how they can be employed judiciously, for example, for sparse Jacobians and to exploit parallelism. We show how, and under what circumstances, automatic differentiation applied to iterative solvers delivers the mathematically desired derivatives. We then show how derivatives that can now be feasibly obtained by computational differenti..