Efcient Discretization and Differentiation of Partial Differential Equations through Automatic Functional Differentiation

High-performance algorithms for PDE-constrained optimization [7] require derivatives of the residual with respect to the design variables. These derivatives are not available from most PDE codes, so to obtain derivatives from an existing code one must apply automatic differentiation (AD) to the code. One alternative approach is to write a new code where low-level calculations are templated on a AD-enabled scalar type [3]. Another approach, which we consider here, i