Developing a derivative-enhanced object-oriented toolkit for scientific computations.

We describe the development of a differentiated version of PETSC, an object-oriented toolkit for the parallel solution of scientific problems modeled by partial differential equations. Traditionally, automatic differentiation tools are applied to scientific applications to produce derivative-augmented code, which can then be used for sensitivity analysis, optimization, or parameter estimation. Scientific toolkits play an increasingly important role in developing large-scale scientific applications. By differentiating PETSC, we provide accurate derivative computations in applications implemented using the toolkit. In addition to using automatic differentiation to generate a derivative enhanced version of PETSC, we exploit the component-based organization of the toolkit, applying high-level mathematical insight to increase the accuracy and efficiency of derivative computations